Abstract

The present study aims to investigate the effectiveness of plasma actuators in controlling the flow around a finite wall-mounted square cylinder (FWMSC) with a longitudinal aspect ratio of 4. The test is conducted in a small-scale closed return-type wind tunnel. The Reynolds number of the experiments, Red, is 500 based on the width of the bluff body and the freestream velocity. The plasma actuators are installed on the top surface and the rear surface of the square cylinder. The induced flow velocities of the plasma actuators are modulated by adjusting the operating voltage and frequency of the high-voltage generator. In this work, particle image velocimetry (PIV) is used to obtain the velocity fields. Furthermore, force calculations are conducted to investigate the effect of using plasma actuators with different driving voltages on the drag force. Our results show that the plasma actuators can successfully suppress flow separation and reduce the turbulent kinetic energy (TKE) in the wake. A correlation between the drag coefficient and the operating voltage of the power generator is also revealed, and the mean drag coefficient is found to decrease with increasing imposing voltage. The plasma actuators can enhance the momentum exchange and the interactive behavior between the shear layer and the flow separation region, resulting in flow reattachment at the free end and shrinkage of the recirculation zone in the near-wake region of the bluff body. Overall, the present study demonstrates the practical effectiveness of using plasma actuators for flow control around FWMSC.

1 Introduction

The flow around a finite wall-mounted square cylinder (FWMSC) has been extensively studied over several decades due to its wide range of applications in numerous fields. This model provides a simplified representation of common obstacles found on vehicles and aircrafts, such as rearview mirrors and landing gears. In recent years, significant progress has been made in understanding the complicated three-dimensional (3D) flow structure around an FWMSC, with numerous studies conducted in this area [15]. The flow structure is composed of four primary types of vortices, namely, the tip vortex, spanwise vortex, horseshoe vortex, and base vortex. The tip vortex is caused by the downwash flow from the free end of the FWMSC, while the base vortex is induced by the upwash flow from the boundary layer. The thickness of the boundary layer can strengthen the base vortex [6,7]. By increasing the submerged length of the bluff body in the boundary layer, the mean drag force and fluctuation lift force will be reduced [3]. Furthermore, the tip and the spanwise vortices will merge near the free end and form an arch-type flow structure [4].

The aspect ratio h/d where h and d represent the height and width of the FWMSC, respectively, plays a significant role in spanwise vortex shedding structures. Specifically, the aspect ratio has a considerable influence on the type of spanwise vortex shedding. When the aspect ratio is smaller than the critical value, the downwash flow becomes relatively strong, resulting in a symmetric type of spanwise vortex. However, under these circumstances, the lift coefficient has a high amplitude but is not periodic. In contrast, when the aspect ratio is above the critical value, the downwash flow becomes weak and cannot dominate the wake structure. Consequently, both symmetric and asymmetric shedding occurs intermittently [2,811]. Although the amplitude of the lift coefficient decreases, it becomes more periodic compared to the previous case. In general, the critical aspect ratio is influenced by the oncoming flow conditions, including the Reynolds number, turbulence intensity, and boundary layer thickness in the bluff body region [1,12], and a suggested value of 2.5 was given for the finite square cylinder [13]. Our profound understanding of the flow structure near the finite-length bluff body enables us to employ methods to control the flow around it, such as suppression of flow separation and drag reduction. The flow control methods can generally be divided into two types depending on the input energy: passive and active control. In addition, active flow control can be further classified into closed-loop control and open-loop control due to the different feedback mechanisms [14].

Compared to active flow control, studies on passive flow control are more commonly conducted due to its easy implementation. In particular, passive flow control methods require no additional energy input, rendering them more cost-effective than their active counterparts. Consequently, a vast number of studies on passive flow control methods have been conducted during the past few decades. These methods primarily involve surface modifications, such as roughness, splitter plates and holes, as well as the use of external elements and geometric modifications in the spanwise direction [11,15,16].

On the other hand, active flow control offers numerous advantages over passive flow control. Passive flow control typically involves the modification of the target's surface structure, which can sometimes be impractical or impossible to perform. Unlike passive flow control, active flow control seeks to introduce extra momentum into the flow field without modifying the surface structure of the designated model, making it a more practical and efficient approach. As a result, active flow control has gained significant attention in recent years as a promising technique for controlling aerodynamic forces and flow structures around finite wall-mounted square cylinders. Wang et al. [3] used a steady slot suction at the free end of an FWMSC cylinder to control the aerodynamic force. The authors applied different suction velocities to reduce the mean drag, fluctuating drag and lift coefficients, and reached a reduction of 3.6%, 17.8%, and 45.5%, respectively. Li et al. [17] performed an experimental study on active flow control by using a dual synthetic jet on the free end of a FWMSC. To generate this synthetic jet, a piezo-electric dual synthetic jet actuator was installed at the leading edge of the free end. The experimental results demonstrated a clear correlation between the control efficiency and the amplitude and frequency of the dual synthetic jet. Moreover, the aerodynamic coefficient and free-end shear flow were effectively suppressed, while the turbulent kinematic energy was significantly enhanced.

The dielectric barrier discharge plasma actuator has recently garnered significant attention due to its characteristics of flexibility, high efficiency, and fast response [18]. A typical plasma actuator consists of two electrodes and a dielectric material between them. Application of high-voltage AC to the electrodes will ionize the air near them, which is subsequently accelerated by the electric field generated by the AC, generating a plasma wind. Numerous studies have been conducted on 2D flows around bluff bodies. For example, Chen and Wen [19] applied three different types of plasma actuators on the D-shaped bluff body, while Zhu et al. [20] numerically studied the performance of installing plasma actuators at different locations on an infinite square cylinder. The previous studies showed that plasma actuator-based flow control could perform well in suppressing vortex shedding and reducing the aerodynamic coefficient for relatively simple flow structures.

Nonetheless, the capability of plasma actuators to control complex 3D flows has not been intensively investigated. In this context, the present study aims to investigate the feasibility of using plasma actuators for active flow control on the FWMSC. Multiple plasma actuators were installed on different surfaces of the FWMSC to enhance our understanding of the effect of plasma actuators on 3D bluff body flows. Three different configurations of plasma actuators are compared to better comprehend the mechanism of plasma actuator control of the flow.

The remainder of this paper is organized as follows: Sec. 2 introduces the experimental design of the model, wind tunnel, plasma actuators and measurement equipment used in the present study. The results, including contours, profiles, statistics and aerodynamic coefficients, are presented in Sec. 3. Finally, Sec. 4 provides conclusions based on the results of the study.

2 Experimental Setup

The experiments are conducted in a return-type wind tunnel with a test section of 250 mm × 250 mm × 1000 mm. The experimental facility comprises an FWMSC made of an acrylic board, plasma actuators, a signal generator, a voltage amplifier, a load cell for force measurement, a pitot tube for point velocity measurement, and a PIV system for velocity measurements.

A pitot tube is placed upstream of the model to measure the freestream velocity. The freestream velocity, U, is approximately 0.4 m/s, so the corresponding Red based on the width of the square cylinder is approximately 500. The corresponding turbulence intensity of the freestream is less than 0.8%. The schematic diagram of the wind tunnel and the arrangement of experimental equipment are shown in Fig. 1(a), and the schematic diagram of the wind tunnel test section is shown in Fig. 1(b).

Fig. 1
(a) Schematic diagram of the wind tunnel and experimental equipment. (b) Schematic diagram of the wind tunnel test section.
Fig. 1
(a) Schematic diagram of the wind tunnel and experimental equipment. (b) Schematic diagram of the wind tunnel test section.
Close modal

2.1 Model Geometry and the Arrangement of Plasma Actuators.

The experimental model used in this study is an FWMSC mounted on the wall of the wind tunnel's test section. The model, composed of acrylic material, had a width (d) of 20 mm and a height (h) of 80 mm. The blockage ratio of the model is approximately 2.6%. The model consists of two plasma actuators installed on its respective surfaces, with plasma actuator 1 located on the top surface and plasma actuator 2 on the rear surface. Detailed configurations of the model are provided in Fig. 2. Both the exposed and encapsulated electrodes of the plasma actuators are made of copper, with a thickness of 0.07 mm. The dielectric material is composed of two layers of Kapton tape, each with a thickness of 0.065 mm, resulting in a total thickness of 0.13 mm. Since this thickness is significantly small compared to the model's width, the impact of the plasma actuators on the flow field can be considered negligible. The plasma actuators are operated by imposing high AC voltage on the exposed electrodes. The power has a sinusoidal waveform with a frequency of 900 Hz and a peak-to-peak voltage of 9 kV. The AC power is generated by a function generator (Agilent 33,522 A) and then amplified by a voltage amplifier (Trek MODEL 610E) for plasma actuator operation. Because the natural vortex shedding frequency is much smaller than the input AC signal frequency, the flow control is considered continuous [21].

Fig. 2
(a) Arrangement of plasma actuators and laser sheets. (b) and (c) Configuration of the two plasma actuators. (d) Top view (left) of the plasma actuator 1 and rear view of plasma actuator 2 (right).
Fig. 2
(a) Arrangement of plasma actuators and laser sheets. (b) and (c) Configuration of the two plasma actuators. (d) Top view (left) of the plasma actuator 1 and rear view of plasma actuator 2 (right).
Close modal

In this work, except for the no-control case, three different cases are experimentally considered to investigate the plasma actuator flow control. In case 1, only actuator 1 is activated, while actuator 2 is turned off. In case 2, actuator 1 is turned off and actuator 2 is turned on. Finally, in case 3, both actuators are turned on.

2.2 Velocity Measurements.

Our experimental process uses the PIV to obtain the velocity fields around the bluff body. The PIV system comprises a CCD camera (VC-12MX) with 4096 × 3072 pixels resolution and a two-pulsed laser (Evergreen, EVG00070). In the wind tunnel experiments, the wind tunnel is seeded by olive oil droplets generated by the TSI 9307 particle generator. The average size of the oil droplet is 0.65 μ m. The planes chosen in this experiment are shown in Fig. 2(a). Along the cylinder height, three planes are arranged within z/d = 1, 2, and 3 at the rear region of the bluff body, also the plane location where y/d = 0 is considered. For each location, 2000 snapshots are recorded for postprocessing. All the PIV experiments are conducted three times, and the data from different experiments shows the same results which can prove the repeatability of the PIV experiments.

2.3 Drag Force Measurements.

Due to the limitation in terms of its sensitivity to the relatively low Reynolds number of this study, the (DACELL-MC15) load cell is used to measure the drag force at Red = 4700 which is utilized to validate the estimated drag force obtained using the momentum-deficit method. Figure 1(b) shows the load cell arrangement in the test section of the wind tunnel. To eliminate low-frequency vibrations caused by the wind tunnel, the load cell is mounted on a flat fixed frame placed on the ground. The sampling frequency of the load cell is 200 Hz. All the force measurements are conducted three times to check the repeatability of the experiments. In addition, the load cell is connected to the bluff body using a metal cylinder.

3 Results and Discussion

3.1 Visualization of the Near-Wake Flow Structure.

Primarily, the induced flow field by the plasma actuators in quiescent air is investigated to gain a deeper understanding of the flow control mechanisms. Figure 3(a) shows that the induced flow from plasma actuator 1 is generated behind the exposed electrode edge and directed toward the encapsulated electrode. Note that the coordinate system for all the plots is fixed on the rear surface where the middle of the intersection between the bluff body and the wall as shown in Fig. 2(a)). Furthermore, two-dimensional flow visualization is conducted in the three different sections (z/d = 1, 2, and 3), as shown in Figs. 3(b)3(d). Two plasma actuators (actuator 2) are positioned at the back of the model, and the induced flow from each actuator is generated at the edge of the respective actuator and directed in opposite directions. The induced flows collide in the centerline behind the model, creating a mixed plasma jet toward the downstream direction (x direction). Here, it is important to note that the induced flow velocities are nearly constant along the wall-normal direction. However, the jet flow is slightly deflected due to a main flow disturbance and configuration of the two exposed electrodes, such as the imperfect parallel alignment.

Fig. 3
The induced flow field in the quiescent air. (a) Induced flow field of plasma actuator 1 at y/d = 0. (b)–(d) Induced flow field of plasma actuator 2 at z/d = 1, 2, and 3, respectively.
Fig. 3
The induced flow field in the quiescent air. (a) Induced flow field of plasma actuator 1 at y/d = 0. (b)–(d) Induced flow field of plasma actuator 2 at z/d = 1, 2, and 3, respectively.
Close modal

The control effects of the plasma actuators could be reflected by the suppression of the free end and the spanwise vortex shedding patterns. Figure 4 exhibits the time-averaged contours of the dimensionless streamwise velocity, wall-normal velocity, and spanwise vorticity in the central lateral plane (y/d = 0). As shown in Figs. 4(a1)4(a3), the flow separates from the leading edge, and a recirculation zone is generated behind the cylinder. This phenomenon is similar to the flow structure reported by Saha [5] with respect to a wall-mounted square cylinder with h/d = 4.

Fig. 4
Time-averaged contours of the streamwise velocity and streamlines (left column), wall-normal velocity (middle column) and spanwise vorticity (right column) for y/d = 0. (a) No-control, (b) case 1, (c) case 2, and (d) case 3.
Fig. 4
Time-averaged contours of the streamwise velocity and streamlines (left column), wall-normal velocity (middle column) and spanwise vorticity (right column) for y/d = 0. (a) No-control, (b) case 1, (c) case 2, and (d) case 3.
Close modal

The results reveal interesting findings for case 1 (only actuator 1 is turned on), where the reattachment flow occurs near the top surface of the bluff body, as illustrated in Figs. 4(b1)4(b3). The separated flow rapidly reattaches to the top surface of the bluff body, causing a change in the shape of the recirculation zone. Notably, the core of the recirculation bubble moves downwards from z/d = 3.4 to z/d = 3, indicating a significant impact on the free shear layer structures and downwash flow characteristics.

For case 2 shown in Figs. 4(c1)4(c3), where actuator 1 is turned off and actuator 2 is turned on, the results identify that the induced streamwise velocity can suppress the upwash flow near the wake region of the bluff body. In addition, the induced streamwise velocity could reduce the adverse flow region in the recirculation zone by injecting high-velocity-induced flow downstream, leading to an increased momentum exchange in the recirculation zone and a decrease in the adverse pressure gradient. Consequently, the recirculation zone is diminished, a behavior that is also reflected by the deformation of the shear layer structure.

As shown in Figs. 4(c1)4(c3), a new shear layer is formed and a smaller recirculation region is formed behind the model. Furthermore, in the region where z/d ranges between 3.5 and 4, there appears to be a strong upwash flow behind the trailing edge of the top surface (i.e., x/d = 0, z/d = 4) in cases 2 and 3, as shown in Figs. 4(c2) and 4(d2). This seems to be attributed to the wall-normal pressure gradient of the new shear layer and the high-velocity region above the bluff body. Generally, a similar tendency is also observed in case 3, as shown in Figs. 4(d1)4(d3).

Figure 5 presents the overall flow visualization behind the model along the horizontal plane (i.e., z/d = 2), indicating the time-averaged contours of streamwise velocity, Reynolds shear stress, and wall-normal vorticity. For the no-control case (Figs. 5(a1)5(a3)), it can be conjectured that the adverse pressure gradient observed behind the bluff body leads to the formation of a wide recirculation zone, which could cause a substantial drag force acting on the bluff body (see Fig. 5(a,1)). As shown in Figs. 5(a2) and 5(a3), the strong variation of Reynolds stress affects a wider wake region downstream of the cylinder, and the mean vorticity contour seems consistent along the centerline of the cylinder. This behavior determines the range of vortex shedding frequency [19].

Fig. 5
Time-averaged contours of streamwise velocity and streamlines (left column), Reynolds stress component u′v′¯ (middle column) and wall-normal vorticity (right column) for z/d = 2. (a) No-control, (b) case 1, (c) case 2, and (d) case 3.
Fig. 5
Time-averaged contours of streamwise velocity and streamlines (left column), Reynolds stress component u′v′¯ (middle column) and wall-normal vorticity (right column) for z/d = 2. (a) No-control, (b) case 1, (c) case 2, and (d) case 3.
Close modal

In case 1, the wake flow field varies a little (see Figs. 5(b1)5(b3)), and the maximum Reynolds stress is notably decreased compared with that obtained from the no-control case (see Fig. 5(b,2)). As shown in Figs. 5(c1)5(c3), when the plasma actuator 2 is turned on, the wake flow structure reveals a significant variation. The recirculation zone in case 2 is suppressed by the control of plasma actuator 2, and the reattachment point moves upstream from x/d = 4 to x/d = 2.5. Furthermore, a substantial variation in the Reynolds stress and mean vorticity is also identified. As shown in Fig. 5(c,2), the maximum Reynolds stress moves upstream from x/d = 4.5 to x/d = 3. The results reveal that the use of a plasma actuator can effectively suppress velocity fluctuations in the wake, resulting in a substantial change in the wake structure, as shown in Fig. 5(c,3). The purpose is to inject high-momentum plasma into the flow field, leading to momentum exchange that accelerates the relatively slow velocity flow in the recirculation zone. As a result, the pressure gradient decreases, effectively suppressing flow separation. The shear layer tends to become narrower and deviate along the centerline behind the cylinder.

In case 3, the results (as shown in Figs. 5(d1)5(d3)) indicate that the recirculation zone becomes smaller, leading to a further decrease in the Reynolds stress downstream. Additionally, the shear layer becomes narrower to both the centerline and the rear surface of the bluff body, demonstrating that case 3 is more efficient than case 2. It can be inferred that among the three cases, case 3 is the optimal control case as it can alter the wake structure significantly. In summary, the results indicate that the plasma actuator on the rear surface plays a crucial role in suppressing the flow separation, inducing significant changes in the wake structure. In addition, the plasma actuator 1 on the top surface also contributes to reducing the turbulent wake.

Figure 6 shows the contour of the TKE profile for each case investigated in the present study. Here, TKE is defined as
TKE=(u)2¯+(v)2¯2U2
(1)

where u and v components are the streamwise and spanwise fluctuating velocities, respectively. Note that TKE and Δ TKE represent the level of the fluctuating velocity and the difference in TKE between the control cases and the no-control case, respectively. In the no-control case, the value of TKE becomes big after reaching x/d = 2 due to the strong vortex-shedding behavior. In contrast, the value of TKE becomes very low in the near-wake region between x/d = 0 and x/d = 2 due to the recirculation area. After activating the plasma actuator control, the maximum value of TKE tends to move upstream. As shown in Figs. 6(b1)6(d1) and 6(b,2)–6(d,2), the plasma actuator increases the strength of TKE near the wake because of the induced turbulent flow, but the range of TKE from x/d = 4 to x/d = 6 becomes narrower compared with the no-control case. The results show that the actuator control reduces the level of TKE downstream, indicating the suppression of the vortex shedding.

Fig. 6
TKE and Δ TKE of the no-control and three control cases (z/d = 2). (a) No-control, (b1) and (b2) represent case 1, (c1) and (c2) represent case 2, (d1) and (d2) represent case 3.
Fig. 6
TKE and Δ TKE of the no-control and three control cases (z/d = 2). (a) No-control, (b1) and (b2) represent case 1, (c1) and (c2) represent case 2, (d1) and (d2) represent case 3.
Close modal

Figure 7 demonstrates the time-averaged contours of the dimensionless streamwise velocity at the planes where z/d = 1 and z/d = 3. The spanwise velocity fields at z/d = 1 and z/d = 3 are shown in Figs. 7(a)7(h), respectively, and it is evident that the overall flow structures are substantially different from one another. The recirculation zone at z/d = 1 looks bigger than that at z/d = 2 and the reattachment point appears around x/d = 5, which is further behind the central plane than where the flow is reattached at x/d = 4. This would be attributed to the separated upwash shear flow from the side of the model, which is also observed by Wang et al. [3] Figs. 7(e)7(h) exhibits the streamwise velocity field at z/d = 3, which is close to the free end of the bluff body. The dark solid lines represent the isolines, which have an M shape, indicating the faster recovery of the wind speed in the central region. Interestingly, as the flow control is made, the recirculation zone moves closer to the centerline of the bluff body, which could be attributed to the highly complicated three-dimensional wake flow near the free end. The free-end vortex shedding would suppress the spanwise vortex shedding and the arch-type vortex would be formed by these two different types of vortex shedding near the free end [4,8,22]. Nevertheless, it is worth noting that the flow structure and the shape of vortex shedding are different at various heights. Our results indicate that the actuator control would be an effective way to suppress complicated vortex-shedding structures.

Fig. 7
Time-averaged contours of the streamwise velocity at z/d = 1[(a)–(d)], z/d =  3[(e)–(h)]. (a) and (e) represent the no-control case, (b) and (f) represent case1, (c) and (g) represent case 2, (d) and (h) represent case 3.
Fig. 7
Time-averaged contours of the streamwise velocity at z/d = 1[(a)–(d)], z/d =  3[(e)–(h)]. (a) and (e) represent the no-control case, (b) and (f) represent case1, (c) and (g) represent case 2, (d) and (h) represent case 3.
Close modal

3.2 Statistical Analysis of the Wake Flow.

Figure 8 shows the profiles of the time-averaged streamwise velocity, the root-mean-square (rms) of the streamwise velocity, the uv¯ component of the Reynolds stress, and the TKE at z/d = 2, x/d = 2, 3, 4, 5, and 6, respectively. As shown in the figure, our findings are consistent with the visualization results but more intuitive. Furthermore, this figure clearly demonstrates the shrinkage of the recirculation zone and the suppression of flow separation. In Fig. 8(a), the mean velocity profiles of the control cases prove to be more significant than that of the no-control case, indicating the reduction in the recirculation area. Figures 8(b) and 8(d) exhibit a double-peaked symmetric structure. The induced separated flow behind the model increases the fluctuating velocity at x/d = 2, which is in turn decreased in the downstream region. In case 3, with the control of both plasma actuators, the fluctuating velocity reaches its minimum value in the control cases, indicating it is the optimal control case.

Fig. 8
Profiles of the time-averaged: (a) streamwise velocity, (b) root-mean-square of the streamwise velocity, (c) Reynolds stress component u′v′¯, and (d) TKE. Results are obtained at z/d = 2, x/d = 2, 3, 4, 5, and 6, respectively.
Fig. 8
Profiles of the time-averaged: (a) streamwise velocity, (b) root-mean-square of the streamwise velocity, (c) Reynolds stress component u′v′¯, and (d) TKE. Results are obtained at z/d = 2, x/d = 2, 3, 4, 5, and 6, respectively.
Close modal

As shown in Fig. 9, the behavior of the vortex shedding frequency is examined by means of performing a power spectral density (PSD) analysis of the streamwise fluctuating velocity at x/d = 1 and y/d = 1 for different wall-normal locations along the height of the cylinder and for different configurations of the plasma actuators. The PSD peak indicates the dimensionless vortex shedding frequency, Strouhal number (St)=0.107, which is similar to the ones found in the literature [11]. The St is defined as fd/U, where f is the shedding frequency. In the case of no-control, a secondary peak appears at around St =0.24 due to the second harmonic [4]. As shown in Fig. 9(a), the strength of the PSD becomes lower with increasing height. At z/d = 3, the peak of the PSD decreases rapidly due to the complex 3D flow behavior near the free end. The separated vortices determine the peak of PSD, and the downwash flow from the free end vortex shedding weakens the vortex shedding as a result of suppressing the strength of the PSD. In addition, Fig. 9(b)9(d) shows the PSD obtained by the three control cases, in which the dominant peak of the PSD exhibited by the no-control case is decreased, forming certain peaks of lower strength, indicating the suppression of the periodic vortex shedding behavior. As shown in Fig. 9(d), the PSD has a noticed reduction in its peaks along the height of the cylinder. It can be also observed from the results that the plasma actuator on the top surface could efficiently strengthen the downwash flow and weaken the spanwise vortex at high elevations.

Fig. 9
Power spectral density (PSD) of the streamwise fluctuating velocity at x/d = 1, y/d = 1, z/d = 1, 2, and 3. (a) No-control, (b) case 1, (c) case 2, and (d) case 3.
Fig. 9
Power spectral density (PSD) of the streamwise fluctuating velocity at x/d = 1, y/d = 1, z/d = 1, 2, and 3. (a) No-control, (b) case 1, (c) case 2, and (d) case 3.
Close modal

3.3 Aerodynamic Performance of Plasma Actuators.

The effect of flow separation can be highlighted in terms of aerodynamic forces acting on the bluff body. Therefore, this section underlines the effect of plasma actuators on the aerodynamic performance (i.e., drag reduction). The momentum-deficit method is used in this study to estimate the drag force [23,24]. This approach utilizes the combination of two fundamental principles in fluid dynamics, i.e., mass and momentum conservation to represent the aerodynamic drag force along the direction of the flow such that
FD=ρδn=1Ny[U(y)(UU(y))]ndy
(2)

where FD is the estimated drag force, ρ is the density, δ represents the separation distance between a measured horizontal (xy) plane and the previous plane, where the drag force is assumed to be extended, U(y) is the average streamwise velocity downstream the cylinder as a function of the spanwise direction at a specific streamwise location in the wake (x/d = d), and N represents the number of measured (xy) planes. Note that in the current formulation, the viscous contributions and the unperturbed pressure loss with respect to the upstream boundary are considered to be negligible. The detailed derivation of the momentum-deficit formula, which is beyond the current paper's focus, can be found in the work of Jones [23]. As mentioned in Sec. 2.3, the load cell is used to perform the drag force measurements at Red = 4700 for the validation of the method.

Figure 10(a) demonstrates the percentage of drag reduction (ΔCD/CDoff) for the flow at Red = 4700 using both load cell measurements and the momentum-deficit method, where CDoff represent the drag coefficient for the no-control case. In the figure, the maximum drag reduction ratio obtained from the load cell measurements reaches a value of approximately 9.1% for case 1, 21.4% for case 2 and 22.7% for case 3. Based on these findings, it can be concluded that case 3, which employs both plasma actuators, exhibits a superior performance at high input voltage compared to case 2, where only the rear surface plasma actuator is used. Notably, as the input voltage decreases, the drag reduction in both cases is eventually converged, which could be attributed to the insufficient induced flow from the top surface plasma actuator at a low input voltage, which fails to promote the reattachment of the separated flow on the surface. It can be observed from the figure that the plots of the estimated drag force reduction obtained from the momentum-deficit method show a similar trend as load cell results with an expected deviation.

Fig. 10
(a) Drag reduction and (b) corrected drag reduction for the flow at Red = 4700; MD represents the momentum-deficit method. (c) Drag reduction and (d) corrected drag reduction for the flow at Red = 500.
Fig. 10
(a) Drag reduction and (b) corrected drag reduction for the flow at Red = 4700; MD represents the momentum-deficit method. (c) Drag reduction and (d) corrected drag reduction for the flow at Red = 500.
Close modal
Moreover, we use the corrected drag coefficient to eliminate the thrust effect caused by the plasma actuators. The ΔCDcorrected is defined as
ΔCDcorrected=ΔFDT12ρU2A
(3)

where ΔFD is the drag force reduction, T is the thrust from the plasma actuators measured in the quiescent air, and A represents the frontal area of the cylinder that is used in the measurement or the estimation of the drag force. The observed drag reduction can be attributed to two different parts: the thrust in a direction opposite to the drag force and the reattachment behavior after flow separation, which yields a decrease in the pressure difference. Here, ΔCDcorrected can correct the drag coefficient after eliminating the thrust effect. As shown in Fig. 10(b), for the flow at Red = 4700, at input voltage of 9 kV, the ΔCDcorrected obtained from the load cell measurements for case 1, 2, and 3 are 4.5%, 13.2%, and 10%, respectively. The ΔCDcorrected for case 1 is low compared with the value obtained from the other two cases, suggesting that the thrust is the main contributor to the observed drag reduction. Moreover, ΔCDcorrected in case 3 is lower than that in case 2, which is due to the effect of the top surface plasma actuator. Similar to the results in Fig. 10(a), the results obtained from the momentum-deficit method show a consistent behavior to those obtained from the load cell.

As shown in Fig. 10(c), the drag reduction plots obtained using the momentum-deficit method for the flow at Red = 500 increase with the increasing of the applied voltage with a similar trend to the flow at Red = 4700. It is worth mentioning that by using the momentum-deficit estimation, our interest is to investigate the behavior of the drag reduction with the increasing of the applied voltage regardless of the expected deviation of the estimated values from the actual ones. These results also indicate that case 3 is more effective at high input voltage compared to case 2. Notably, the results from Fig. 10(d) reveal that although the ΔCDcorrected plots show a similar trend to the flow at Red = 4700, at low applied voltages, case 2 shows noticeably higher values as compared with case 3.

4 Conclusions

The present study aimed to experimentally investigate the plasma actuator effect on the near-wake flow structure and aerodynamic performance of a wall-mounted square cylinder with an aspect ratio of four at a low Reynolds number (Red = 500). The cylinder was equipped with plasma actuators on the top and rear surfaces, and three control cases were used to enhance the control efficiency of the 3D wake structure. The near-wake structure was studied both qualitatively and quantitatively by means of mean velocity, fluctuating velocity, Reynolds shear stress, turbulent kinetic energy, and power spectral density analysis.

The visualization results showed that all three control cases can suppress the flow separation from the sharp leading edges of the square cylinder, with the control case 3 (having both plasma actuators) performing exceptionally well. The plasma actuator on the top surface of the cylinder causes the reattachment behavior that can be observed at the free end, while the plasma actuator on the rear surface vastly reduces the recirculation zone behind the bluff body. The reattachment point moves from x/d = 4.2 in the uncontrolled case to x/d = 2 in the control case 3, which exhibits the best control efficiency.

Furthermore, the turbulent kinetic energy results revealed that the plasma actuators can effectively reduce the value of turbulent kinetic energy downstream. However, the chaotic-induced flow obtained from the plasma actuators is found to slightly increase the turbulent kinetic energy in the near-wall region. The obtained statistical results are consistent with the visualization results, indicating that all control cases contribute to the suppression of the flow separation.

The power spectral density analysis also showed that all three control cases can weaken the vortex shedding, with the plasma actuator on the top surface strengthening the downwash flow. Furthermore, the drag force measurements demonstrated that all control cases facilitate drag reduction, with the maximum reduction of 9.1%, 21.4%, and 22.7% in the three controlled cases, respectively, for the flow at Red = 4700. Here, case 3 exhibited the optimal drag reduction performance within various driving voltages. A similar behavior of the drag reduction obtained from the momentum-deficit method was found for the flow at Red = 500.

Overall, our findings showed that case 3, which is controlled by both plasma actuators, is the most effective approach for controlling the flow. This is because the induced flow from the plasma actuators can efficiently exchange momentum, accelerating the flow in the recirculation zone and reducing the drag force.

Acknowledgment

This research initiative, carried out in 2022 and supported by the Ministry of SMEs and Startups, falls under the SME Technology Innovation Development Project.

Funding Data

  • Human Resources Program in Energy Technology' of the Korea Institute of Energy Technology Evaluation and Planning (KETEP), granted financial resource from the Ministry of Trade, Industry & Energy, Republic of Korea (Grant No. 20214000000140; Funder ID: 10.13039/501100007053).

  • National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (Grant No. 2019R1I1A3 A01058576; Funder ID: 10.13039/501100003725).

  • SME Technology Innovation Development Project (Project No. S3313372).

Data Availability Statement

The data that support the findings of this study are available within this article.

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