Active Flow Control and Its Applications in Supersonic Boundary Layer

Abstract

Boundary layer transition is a typical aerodynamic phenomenon in supersonic flow that refers to the transition of the boundary layer from laminar flow to turbulent flow. The instabilities and transition mechanisms are complicated. A turbulent boundary layer has an associated higher energy content more momentum and, therefore, is less prone to be separated. Furthermore, accurate and fast transition in the flow over the compressor blades in turbo machinery provides significant flow mixing, resulting in an increase in engine performance. In addition, the development of the scramjet made it possible to use plasma actuators as turbulator to increase the turbulence within an isolator and increase combustion efficiency. Thus, different methods of boundary layer transition have been proposed. The focus of this chapter is a low Reynolds number supersonic boundary layer and its interaction with an active flow control device. The Plasma-Based Actuator’s high repetition rate enables itself as an unsteady control mechanism to address the unsteady flow features. Moreover, its strong forcing makes it suitable for flow control applications in the high-speed flow regime, especially the supersonic boundary layer.

1. Introduction

Boundary layer transition is a typical aerodynamic phenomenon in supersonic flow that refers to the transition of the boundary layer from laminar flow to turbulent flow. The instabilities and transition mechanisms are summarized in detail in Ref. [1]. The effective control of the laminar-turbulent transition is crucial to increase the resistance to the adverse pressure gradient resulting from the shock in the shock wave/boundary layer interaction (SWBLI) in Ref. [2]. The major difference between laminar and turbulent flow is the velocity profile. A turbulent boundary layer has more momentum and is less prone to be separated by the disturbance. Furthermore, accurate and fast transition in the flow over the compressor blades in turbo machinery provides significant flow mixing, resulting in an increase in engine performance. In addition, the development of the scramjet made it possible to use plasma actuators as turbulator to increase the turbulence within an isolator and increase combustion efficiency. Thus, different methods of boundary layer transition have been proposed. In general, boundary layer transition can be classified into three categories based on different mechanisms that act separately or in combination: natural transition, bypass transition, and separation-induced transition. The transition path is summarized in Ref. [3], as shown in Figure 1. In either pathway, the final state is turbulence, which enhances mixing and leads to a higher-momentum boundary layer. The focus of this work is to investigate the ability of a plasma actuator array to produce disturbances in the transient growth for the purpose of promoting bypass transition.

Figure 1.

Five boundary layer transition paths to turbulent flow.

Plasma-based actuators (PBAs) have attracted significant interest in the last three decades as an active flow control technology. Due to their simplicity, sufficient frequency bandwidth, fast response, and zero-drag compensation [4], they are superior to all passive control devices and several semiactive control devices, which are complex, heavy, noisy, and have vibrating moving parts. PBAs have various discharge types, such as a thermal perturbation induced by surface arc discharge in Ref. [5], wall-jet induced by dielectric barrier discharge in Ref. [6], and a high-speed synthetic jet induced by cavity discharge in Ref. [7], affecting the characteristics of the supersonic boundary layer. In particular, surface arc plasma actuators (SAPAs) are considered the most suitable for high-speed flow regimes due to their significant heating effect. Comprehensive reviews of these actuators can be found in Ref. [8, 9, 10].

Preliminary investigations of boundary layer control by PBAs have focused on transition delay in Ref. [11] because transition promotion is considered an undesirable effect in boundary layer control. Generally, a laminar boundary layer reduces the severity of heat transfer and drag friction. Therefore, a growing number of studies have focused on maintaining the laminar boundary layer state in Ref. [12, 13]. However, in some hyper- and supersonic applications, a long-duration laminar/laminar-turbulent transition region can cause detrimental impacts on vehicle performance. Thus, boundary layer transition promotion is also required. The basic method is to generate a fast turbulent spot with sufficient intensity and frequency. Experiment studies in Ref. [14, 15] have shown that both promotion and delay of boundary layer transition can be achieved by using a glow-discharge actuator. Two plasma actuators were used in a flat plate to influence the growth of the transition. The first actuator located downstream of the leading edge was operated in pulsed mode to create strong Tollmien-Schlichting (TS) waves, resulting in turbulence promotion. Two steadily operating actuators further downstream significantly damped the perturbations, suppressing the growth of the TS waves in the transition delay. However, the mainstream velocity was not specified.

In recent works [15, 16], SAPAs were used as a source of perturbations in supersonic flow, especially for a new circuit [17] with a parallel capacitance connection, which enables the PBAs to release sufficient intensity rapidly. This effect can lead to a rapid transition of the boundary layer to turbulent flow, either generating longitudinal streaks [18] or vortex structures that eventually develop into turbulent spots [19]. Recently, numerous publications have demonstrated the successful transition of the boundary layer to turbulent flow on a flat plate using plasma actuators based on surface arc discharge. The effect of steady and unsteady thermal perturbation on the transition of the boundary layer in a Mach 1.5 flat-plate flow is investigated in Ref. [20]. The results indicated that the transition process was enhanced by the actuators, suggesting that the perturbed boundary layer showed signs of transitioning to turbulence, although it remained in transitional flow at the end of the plate. More recently, the PBA’s high repetition rate has been used as an unsteady control mechanism to address unsteady flow features. A SAPA array driven by altering the frequency was proposed in Ref. [21] It can modify the boundary layer condition upstream by a ramp-induced separation shock in Mach 2 flow. Although the energy of a single pulse was very low, a significant vortex effect was observed in the boundary layer. After the activation of the plasma actuator, numerous periodic streamwise vortices were produced in the high-frequency actuation mode, resulting in the transition to turbulent flow of the boundary layer.

In this chapter, SAPA arrays are used in an experiment to perform boundary layer transition on a flat plate at Ma = 3. Several different frequency modes are examined. The ability to control the boundary layer transition is visualized by high-speed schlieren snapshots. Our objective is to demonstrate a new approach to using pulsed SAPAs to achieve fast transient growth in a supersonic laminar boundary layer flexibly and rapidly and reveal the underlying mechanism of supersonic boundary-layer transition by using this type of active flow control stratagem.

2. Supersonic boundary layer physics

The experimental data were collected in a supersonic wind tunnel with a fixed Ma number. The axisymmetric exit has a 300 mm outlet diameter and expands the flow to Mach 2.0 or 3.0 by using a different contoured nozzle. Two inspection windows are assembled on both sides of the test chamber for flow visualization. Therefore, optical measurement techniques and laser perturbations can have access to the core area of the test section. The wind tunnel is started by a circular membrane-breaking device with an electrical switch. The pump sets consist of three pump types, including water ring pumps (operating range from 0.06 bar to the local atmospheric pressure), sliding vane pumps (operating range from 0.03 to 0.08 bar), and root pumps (operating below 100 Pa). A schematic diagram of the wind tunnel structure is shown in Figure 2 with a picture on the right.

Figure 2.

Schematic diagram and picture of the supersonic wind tunnel structure.

The air inside the vacuum tank was pumped out to achieve a vacuum with a pressure of 5–10 Pa, enabling running times of 2.5 s. A stable supersonic flow with a Mach number of 3.0 was generated during the experiments, with a total pressure of 95.6 kPa and a total temperature of 296 K. In the core test region, the static pressure Ps and static temperature Ts were 2.61 kPa and 106 K, respectively. The velocity of the supersonic free stream was 618 m/s, resulting in a unit Reynolds number of 7.41 × 106 m⁻¹. The operating parameters of this facility are listed in Table 1.

Parameter	Description	Quantity
Ma	Free-stream Mach number	3
$P_0$,(Pa)	Stagnation pressure	95,600
$T_0$(K)	Stagnation temperature	296
Ps(Pa)	Static pressure	2612
Ts(K)	Static temperature	106
$\rho$($\mathit{kg}/m^3$)	Density	0.0856
U($m/s$)	Freestream velocity	618
$\mu$($N\bullet s/m^2$)	Viscosity coefficient	7.43 × 10^−6
Re($1/m$)	Reynolds number per meter	7.41 × 10^6
t(s)	Running time	2.5

Table 1.

Flow parameters.

A Z-type light route was used in the schlieren investigations, as shown in Figure 3. A Gloria 500 W Xenon bulb provided illumination. The schlieren images were captured with a Phantom V2512 ultra-high-speed camera with a maximum resolution of 1280 × 800 pixels. A field of view of 512 × 256 pixels was adopted in the experiment. The image acquisition frequency was 50 kHz with 1 μs minimum exposure time to freeze the boundary layer features. Figure 4 shows a top view of the schlieren system.

Figure 3.

Wind tunnel with diagnostic system.

Figure 4.

Schlieren system (top view).

Prior to the analysis, it is essential to investigate the morphology of a fully developed and undeveloped supersonic boundary layer and discuss the flow field. The boundary layer was developed on a flat plate with a sharp leading edge, installed in the core test section at zero angle of attack. The dimensions of the plate were 440 × 110 × 20 mm.

Figure 5 shows images of the development of a natural boundary layer on a completely smooth flat plate (length = 440 mm) in a parallel flow at zero incidences without any intrusive measurements and plasma actuators. Note that the inspection window is smaller than the plate; thus, only part of the flow field can be captured. Therefore, the development of the supersonic boundary layer was displayed separately. Figure 5(a) shows the side view of the boundary layer ranging from x = 0 mm to x = 130 mm, corresponding to the leading edge of the flat plate (fore-plate). The boundary layer is very thin initially and appears almost uniform with no turbulent structure. It can be concluded that the supersonic boundary layer is in the laminar state. Figure 5(b) shows the side view ranging from x = 130 mm to x = 285 mm (mid-plate). The boundary layer appears as a straight, bright strip immediately above the flat surface; its growth instability leads to the formation of a small turbulent structure, corresponding to a laminar-turbulent transient boundary layer. Unlike in Figure 5(a), turbulent flow is observed in Figure 5(b). Thus, a natural transition occurs in the region x = 130 to 285 mm, after which the flow becomes fully turbulent. In the rear part of the flat plate (rear plate), ranging from x = 285 mm to x = 440 mm (Figure 1(c)), a more rapid increase in the boundary layer instability occurs due to more large turbulent eddies in the near-wall region. Thus, a fully turbulent region is observed after x = 285 mm.

Figure 5.

Base flow on a flat plate (a) fore-plate (b) mid-plate (c) rear plate.

The I_rms for each part of the flat plate are shown in Figure 6. The leading edge of the flat plate is considered the origin of the coordinate system, with the positive x-axis pointing in the streamwise direction, and the positive y-axis pointing in the wall normal direction with respect to the surface. Due to the short camera exposure time and large image ensemble, the boundary layer is frozen with a shaped edge with respect to the mainstream flow, as shown in the contours of the I_rms (normalized magnitude) in Figure 6. The line connecting the lower I_rms value (above 1) along the wall can be taken as the border of the boundary layer. The contours of the I_rms for the fore plate are shown in Figure 6(a), which agree with the fact in the raw schlieren image. The thickness of the boundary layer obtained from the I_rms has not increased, and its average value is very close to the theoretical value of a laminar boundary layer. The contours of I_rms also have the same magnitude in the wall-normal direction owing to the small adverse pressure gradient in the fore-plate. Figure 6(b) the I_rms contours have moved a considerable distance forward after 170 mm, and the width of I_rms from 1 to 1.5 count has thickened substantially. The raising width corresponds to the turbulent structures in the raw schlieren image, and their thickness is even larger downstream. Thus, the transition point can be determined as the point where the I_rms contours move up at approximately 170 mm. The final state of the boundary layer can be inferred from Figure 6(c). Its thickness according to the I_rms continues to increase to a maximum value of 13.5 mm at the end of the flat plate. Two contours with higher I_rms values (ranging from 1.5 to 2 and from 2 to 2.5) move up after x = 305 mm, indicating significant vortical activity in the rear part of the flat plate. The I_rms is very high in the last region, indicating that a fully turbulent boundary layer has developed in the rear plate. The I_rms enables the analysis of the transitional region and the boundary layer state to quantify the effect of the SAPAs on boundary layer transition.

Figure 6.

Contours of the I_rms for boundary layer flow on a flat plate (a) I_rms intensity of the fore-plate (b) I_rms intensity of the mid-plate (c) I_rms intensity of the rear plate.

The supersonic boundary layer’s response to a pressure gradient is also affected by viscous forces, which are often represented by the wall-shear stress or the skin-friction coefficient. The skin-friction coefficient for a flat-plate turbulent boundary layer is a significant function of the Mach number and decreases rapidly as the Reynolds number increases. Because shear forces tend to oppose the retardation effect, we can infer that the resistance of a laminar boundary layer to an imposed pressure gradient decreases with increasing Reynolds number. The situation is more subtle in the turbulent boundary layer, even at a moderate Mach number. Therefore, the behavior of boundary development is usually been characterized by assuming a perfect-fluid model.

3. Active flow control-surface arc plasma actuator

The surface arc plasma actuator has two main configurations, one is a horizontal arrangement, as shown in Figure 7(a), where two cylindrical metal electrodes are flush mounted on an insulator to ensure that the surface is flat without disturbing the original boundary layer flow field. Another arrangement is a recessed layout, as shown in Figure 7(b). The advantage of this layout is that the arc can be avoided blowing off by the incoming supersonic boundary layer flow. The disadvantage is that the cavity will have a certain disturbing effect on the original boundary layer flow field, which will easily confuse the effect of active flow control and cavity control. The two metal electrodes are connected to the positive and negative side of the power supply, thus forming the cathode and anode, and through the load provided by the power supply, a potential difference is formed between the cathode and the anode, while an electromagnetic field is formed in the space above the surface. When the voltage applied between the electrodes exceeds a certain threshold, the air near the electrodes is pierced to form an arc-shaped discharge channel, emitting a dazzling white light and releasing electrical energy in the form of heat rapidly to form a transient explosion effect (as shown in Figure 8). Because of the arc-like shape of the discharge channel, this discharge is also known as an arc discharge. The discharge produces two types of disturbance structures, a shock wave and a localized thermal gas bubble. Because it is a high-voltage pulse discharge, there is a certain amount of electromagnetic interference (EMI) and anti-interference treatment is required. The most common method currently used is to wrap all the conductors in an electromagnetic protective wire jacket and install a grounding electrode near the discharge electrode to absorb most of the electrons. There is also a variant of the surface arc discharge actuator structure while the discharge electrode is placed in a concave cavity with a small hole open into the surface. As the application of the discharge, certain hot jets ejected from the hole to the bottom of the boundary layer as a source of disturbance. This active flow control device is also called plasma synthetic jet actuator, its effect on the control mechanism is also completely different from the surface arc plasma actuator.

Figure 7.

Schematic diagram of the surface arc discharge actuator structure. (a) flush mounted layout (b) cavity layout.

Figure 8.

The evolution of surface arc discharge in atmospheric air.

A schematic diagram of the circuit system is shown in Figure 9. The external circuit system is powered by a high-voltage pulsed power supply and a voltage DC power supply. The high-voltage pulsed power supply is to produce a breakdown voltage to form a steady or pulsed arc between the anode and cathode. The voltage varies from a few kilovolts to tens of kilovolts depending on the ambient pressure. The DC power supply is to increase the energy deposition in the arc and to charge the capacitor beforehand.

Figure 9.

External circuit system.

Figure 10 shows the evolution of the arc pattern when using the above external circuit system with 1 mm electrode spacing. The DC power output voltage is 1.5 kV and the capacitance is 2 μF. To highlight the arc structure, the camera exposure time was reduced to obtain a black background, and the high-speed camera exposure time was set to 1.75 μs. t = 0 μs was set as the trigger of the actuation, and a bright white light was generated between the two electrodes in the figure (anode on the left and cathode on the right) indicating the generation of the surface arc. The maximum arc light intensity and arc area are reached at t = 2.49 μs after the discharge is generated. As the voltage decreases rapidly, the arc light fades and looks like a dumbbell shape, indicating that the arc energy is gradually dissipating into the air. The intensity of the spot near the cathode decays more rapidly than that near the anode. At t = 98.8 μs, the bright light is not visible and the discharge process is considered to have been terminated.

Figure 10.

The evolution of surface arc.

Surface arc discharge is a rapid process of air breakdown to form a steady or pulsed arc between the anode and cathode. TGB and precursor shock (PS) are two major macroscopic characteristics that are generated in the discharging process while the former is mainly influenced by atmospheric pressure [22] and arc length. Figure 11 shows the evolution of TGB and PS produced by a single SAPA with three different arc lengths. The measurements were performed at the same low pressure (12.24 kPa) as during the wind tunnel operation and the actuation frequency is 500 Hz. Here the variation in arc length is obtained by increasing the gap △Z between two electrodes. It should be noted that the maximum distance between electrodes was verified to be 10 mm at low ambient pressure, beyond which it can hardly break down the air to form an arc discharge. Thus the △Z between two electrodes was selected to be 3, 5, and 10 mm for case_1, case_2, and case_3, respectively. These images are captured with an exposure time of 1 μs and a frame size of 640 × 256 pixels, respectively. The resolution of the images is 0.93 mm/pixel, and the interval is about 10 μs. The recording is triggered at the start of the discharge using a DG 535 synchronous controller. The TGB is visible at 30 μs because, at prior times, it is overlapped by the arc light glow and characterized by a clean regular elliptical hemisphere compared to the following snapshots. About 260 μs after the trigger of discharge, more turbulent structures and sharper boundaries inside the TGB can be observed. Later, it becomes more turbulent in the last two snapshots and slowly grows upward.

Figure 11.

Evolutions of TGB for different Δ Z in quiescent air.

As the discharge occurs in a Ma = 2 flow, a dazzling white light can be seen at first, as shown the Figure 12. The shock wave and the thermal gas bubble also can be seen in the schlieren image. At this moment, the internal structure of the thermal gas bubble is clear, with a small height and a regular oval shape, moving downstream with the incoming flow with a propagation speed of about 520 m/s. The morphology of the thermal gas bubble transformed to turbulent because of the shear effect.

Figure 12.

Evolutions of TGB on a flat plate in a supersonic flow (ma = 2).

Figure 13 shows the diagram of the TGB evolution from 40 to 140 μs. At t = 40 μs, although the thermal bubble shape changes, it is still a monolithic structure and does not appear to shed larger vortices. At t = 80 μs, a clear secondary turbulent structure can be seen. The thermal bubble has little momentum in the generation process and the thickness is much greater than the supersonic boundary layer. The upper structure is subjected to higher shear stress and continues to move forward. The lower structure is subjected to shear from the upper layer and hysteresis occurs to form a secondary vortex structure, similar to the vortex shedding that occurs when a large-scale turbulent structure is subjected to a strong disturbance. In addition, the secondary structure breaks down further into smaller-scale structures due to free shear. Thus, the original thermal gas bubble is compressed in the vertical direction.

Figure 13.

Spatial gradient evolution of the TGB evolution.

Figure 14 give typical PLS images of the thermal bubble for a surface arc plasma actuator under supersonic incoming flow conditions at Mach number 2, yielding the same evolutionary process that matches the schlieren image. At t = 25 μs, a distinct hemispherical black spot can be observed downstream of the actuator location, which can be determined as the hot bubble structure, as the hot bubble is hotter and denser, where the applied molecule particles rapidly condense to form a high density shadow, which in turn appears different from the surrounding black area in the PLS image. The shock wave is also accurately captured by the PLS technique due to its high density and can be clearly seen in the image as an umbrella-shaped shock wave above the thermal gas bubble. At t = 25 μs the shape of the thermal bubble starts to change and a small number of large-scale vortex structures are derived, these also show the same black spots as the original thermal bubble.

Figure 14.

PLS results of thermal gas bubbles under supersonic incoming flow conditions (Ma = 2).

4. Applications of surface arc plasma actuator on supersonic boundary layer

In this section, SAPA arrays are used in an experiment to perform boundary layer transition on a flat plate at Ma = 3. Three different frequency modes are examined. The ability to control the boundary layer transition is visualized by high-speed schlieren snapshots and semiquantitatively evaluated by image processing. Our objective is to demonstrate a new approach to using pulsed SAPAs to achieve transient growth in a laminar boundary layer flexibly and rapidly and reveal the underlying mechanism of boundary-layer transition.

The image of the first two pulses is selected to demonstrate the flow evolution of the laminar boundary layer with 10 kHz actuation frequency, as shown in Figure 15. The images of the flow field were acquired at 50,000 fps with an exposure time of 1 μs. The first snapshot captures the glare from the electric arc, which normally lasts a few microseconds, and the temporal delay between the first image and the high-voltage trigger should be a few microseconds. Thus, it should be noted that the first image at t = 0 does not overlap precisely with the high-voltage trigger of the SAPAs. Thus, the first snapshot is used as the temporal origin for the discussion. At t = 0 μs, tiny thermal gas bubbles (TGBs) have already been produced around the electrodes because of the local Joule heating effect, but the laminar boundary layer is unchanged. At t = 20 μs, the discharge process is complete, and the TGBs with a height of y = 0.2 mm have traveled around x = 90 mm downstream from the actuator. The precursor shockwave (PS) is expanding at Ma = 1.0, forming an umbrella shape above the TGBs. In the following snapshots, until t = 80 μs, the laminar nature of the boundary layer is unaffected because no distinct turbulent pattern is observed at the surface of the flat plate. As a result, it is assumed that the SAPAs did not affect the transition of the boundary layer within a certain distance downstream of the actuators. After propagating at about 100 μs, the flickering wakes of the TGBs indicate the generation of trailing vortices as the second pulse is observed in Figure 15(f). At t = 120 μs, the TGBs have traveled a distance of approximately 60 mm downstream of the actuators and have elongated into a long strip shape, with the major axis pointing toward the upper-right quarter. Trailing vortices are produced following the primary TGBs, contributing to a boundary layer with large displacement thicknesses and higher freestream streamlines. In the last snapshot, the TGBs appear as a turbulent structure, unlike in the other images. They move a distance of 80 mm and eventually leave the field of view.

Figure 15.

Schlieren image of the boundary layer development with actuation in a Ma = 3 flow.

The I_rms for 10 kHz reputation is shown in Figure 16. It has a range of 1 to 2.4 counts. This range was selected to determine the I_rms distribution in the near-wall region. The results show substantial differences from the baseline in Section 3.1, which has a stable laminar state that lasts until x = 170 mm. The boundary layer upstream of the actuators is in the laminar state and has a thickness of approximately 1 mm. As the SAPAs are activated, the disturbance of the downstream boundary layer increases significantly. A slight increase in the displacement thickness and the pulsation in the boundary layer is observed, unlike in the raw schlieren images. It is likely caused by the consecutive pass-throughs of the TGBs. In Figure 10, the black bar at x = 80 mm downstream of the actuators indicates where the near-wall region has a much higher I_rms (> 1.6) than in the incoming laminar boundary layer and the downstream region. These peak I_rms contours occur from x = 85 mm to x = 130 mm, corresponding to the stronger fluctuation in the density gradient, indicating the formation of a shear layer with higher velocity fluctuations after the actuators have been activated. A closer inspection of the I_rms value in the entire range of the shear layer shows a small subregion close to the surface where the I_rms values are noticeably lower than in the above region, namely the separated shear layer. The thickness of the boundary layer is greater downstream of the shear layer as the turbulence increases at approximately x = 140 in agreement with the raw schlieren images. The observed increases in the boundary layer thickness and the I_rms values indicate that the transition zone has moved upstream after the activation of the SAPAs. The semiquantitative schlieren results confirm the excellent performance of the SAPAs for accelerating the transition by approximately 30 mm in this case. It should be noted that when SAPAs are used to trip the flow, an adequate distance must be chosen to allow the formation of vortices to impact the boundary layer. This distance is crucial. If the SAPAs are placed too far ahead, the laminar flow region is reduced, which increases the drag. Placing the devices far too close to the desired transition location renders them ineffective.

Figure 16.

The RMS of the Schlieren intensity field (I_rms) for 10 kHz reputation actuation.

The above content demonstrated that surface arc discharge led to the formation of TGBs and streamwise trailing vortices in the boundary layer, strongly affecting its stability and inducing laminar-turbulent transition. The I_rms values for different actuation frequencies (20, 40 kHz) are compared in Figure 17. Due to the interaction with the TGBs, the near-wall region downstream of the actuators has substantially higher I_rms values than the region of the incoming laminar boundary layer, which agrees with the 10 kHz reputation actuation results in Figure 16, namely the shear layer. Its streamwise movement increases as the actuation frequency increases. A comparison of the locations with high I_rms values reveals that high-frequency actuation results in a short shear layer in the streamwise direction. Thus, a faster transition process occurs at higher actuation frequencies. Moreover, the peak I_rms for 20 and 40 kHz actuation exceeds 10, whereas that for 10 kHz actuation (Figure 16) is about 2.4. The increase in the peak I_rms suggests that strong density fluctuations occur downstream of the actuators. In compressible flow, the velocity and density fluctuations are correlated; thus, increased velocity fluctuations are expected in this region. As plasma actuation occurs, numerous periodic streamwise vortices are produced, especially at high-frequency actuation, resulting in an enhancement in the mixture and the momentum transfer in the boundary layer. This explains why the transition to turbulent is relatively fast at high frequencies.

Figure 17.

Contours of I_rms for boundary layer development with different actuation frequencies (a) f = 20 kHz (b) f = 40 kHz.

5. Summary

An experimental study was performed to explore the effects of a SAPA array on boundary-layer transition on a flat plate. High-speed schlieren images and high-frequency pressure measurements were obtained. The RMS results of the schlieren intensity field and dynamic pressure yielded valuable insights into the ability of the SAPAs to induce laminar-turbulent transition.

A natural laminar to the turbulent transition of a supersonic boundary layer on a flat plate for Ma = 3 flow was investigated using the schlieren system with a minimal exposure time and a high image acquisition rate. The results indicated that the SAPAs achieved laminar to turbulent transition using a high repetition rate. The pressure spectra of the locations downstream of the actuators had the same magnitude of the characteristic frequency of the turbulent boundary layer as in the baseline condition, indicating that a transition from laminar to turbulent flow had occurred. In addition, the frequency range widened because many streamwise vortices were present in the boundary layer while the actuators were operating. Two higher actuation frequency modes were compared to determine the frequency effect on the laminar-turbulent transition. The I_rms results indicated that the transition location moved upstream as the actuation frequency increased; however, further solid evidence through direct measurements is needed.

Although we captured the laminar-turbulent transition of a supersonic boundary layer using high-frequency SAPAs, the pressure measurements and schlieren observations did not provide sufficient insights into the velocity profile and the scaling properties of the boundary layer. In the future, we plan a parametric investigation of the effects of the velocity characteristics. Particle image velocimetry could be used to investigate these flow fields in detail. In addition, the delay of the laminar boundary layer control by the plasma actuators should also need to be concerned.

Acknowledgments

The authors gratefully acknowledge the National Natural Science Foundation of China (NSFC) and China Postdoctoral Science Foundation (CPSF) for the financial support under Grant No. 11902360 and Grant No. 2021 M702676.