Control of vortex shedding from a blunt trailing edge using plasma actuators

Experimental Thermal and Fluid Science 46 (2013) 199–210

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Control of vortex shedding from a blunt trailing edge using plasma actuators Giovanni Nati, Marios Kotsonis, Sina Ghaemi ⇑, Fulvio Scarano Department of Aerospace Engineering, Delft University of Technology, Kluyverweg 2, 2629HT Delft, The Netherlands

a r t i c l e

i n f o

Article history: Received 30 June 2012 Received in revised form 18 December 2012 Accepted 19 December 2012 Available online 31 December 2012 Keywords: Blunt trailing edge Dielectric barrier discharge Plasma actuator Vortex shedding Time-resolved PIV

a b s t r a c t An experimental investigation on the use of plasma actuators for vortex shedding suppression is performed. The vortex shedding phenomenon at the blunt trailing edge of an elongated D-shaped body is specifically investigated. The study is focused on the laminar boundary layer regime on an elongated D-shaped flat plate of 12 mm thickness at free-stream velocity up to approximately 10 m/s. Dielectric barrier discharge plasma actuators are utilized in several geometrical configurations at the trailing edge of the plate and are operated in continuous and pulsed mode. Several operational parameters such as applied voltage, carrier and pulse frequency and duty cycle are investigated. Results reveal that tangential actuation both in the downstream or upstream direction yields very limited effects on the coherent organization in the wake. Instead, symmetrical actuation from the base edges towards the wake centerline, proved to be very effective prompting a more detailed study of this actuator configuration. At external flow conditions, the reduction of the Kármán wake component is monitored by the modal energy spectrum obtained from proper orthogonal decomposition of PIV data in the stream-wise/wall-normal plane of the developing wake region. The suppression of coherent vortex shedding is further ascertained with time-resolved visualizations obtained by high-speed PIV and spectral analysis conducted with hot-wire anemometry. In order to gain a complete understanding of the forcing mechanism, the velocity field induced by this actuator configuration is additionally investigated by means of high-speed PIV measurements conducted in initially quiescent flow. It is verified that the suppression mechanism involves the breakup of communication between the two shear layers simultaneously to moderate momentum addition into the recirculation area. Ó 2013 Elsevier Inc. All rights reserved.

1. Introduction The phenomenon of vortex shedding is observed in several cases of flow around solid objects. It is typically observed in the wake of two- or three-dimensional bluff bodies, as well as in the wake of streamlined objects (such as airfoils) at low or high incidence angles depending on Reynolds number [1]. The phenomenon was first described by von Karman and it is known as the Bènard– Kármán vortex street [2]. The general topology of the Bènard–Kármán vortex street, consists of counter-rotating vortices shed alternatively from both sides at a specific frequency [3]. The shedding frequency was first measured by [4] where it was found to scale with the Reynolds number. The large coherent vortices shed in the wake of bluff bodies result in increase of base drag, fluctuations in lift, undesired structural vibration and increased acoustics noise emissions [5,6]. A specific category of aerodynamic bodies subjected to vortex shedding involves airfoils with truncated trailing-edge typically

⇑ Corresponding author. E-mail address: [email protected] (S. Ghaemi). 0894-1777/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.expthermflusci.2012.12.012

used in wind turbine blades. This type of airfoil is used when higher structural strength, lower weight or reduced manufacturing complexity is required [7]. In these cases it becomes relevant to explore possible methods to attenuate or suppress the negative effects of the strong vortex shedding due to the flow separation at the sharp corners of a blunt trailing-edge. The flow control techniques can be divided into three main categories of passive, active open-loop and active closed-loop techniques [8]. All three categories have been used in research studies for the attenuation or suppression of vortex shedding from aerodynamic bodies [6]. Additionally a classification can be made on the flow mechanisms, which are being utilized/manipulated, by these techniques in order to achieve the shedding attenuation. These are: break up the cross-talk between the two shear layers, addition of circulation in the separation region near the base, and control of the stability of the alternate vortex shedding in order to promote faster breakup [9]. A brief description of efforts for vortex shedding control is given here. A comprehensive review on these techniques is provided by Choi et al. [6]. Passive techniques can be defined as techniques where no power input is applied. Typically these methods make use of surface modifications by addition of fixed or freely moving

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bodies in order to manipulate the wake. Shih et al. used roughness elements on circular cylinders for Reynolds numbers up to 8 million [10]. The goal was to promote turbulent flow in order to break the spanwise coherence of the vortex sheet. Lee et al. used helical wires on a cylinder at Reynolds of up to 50,000 in order to fix the separation point in a 3 dimensional loci thus breaking up the spanwise coherence [11]. Akilli et al. attempted to break the communication between the two shear layers in the case of an elongated D-shaped body using splitter plates [12]. In a similar scenario Dalton et al. used small secondary control cylinders [13] in order to influence the shedding characteristics of a larger primary cylinder with promising results. Active open-loop techniques are defined as cases where there is external power input using an actuator, yet no information from the flow is used (no sensor). In contrast active closed-loop techniques involve the use of sensors and control algorithms in order to drive the actuator. Several studies have been published on active control of vortex shedding. Beak and Sung used mechanical oscillations from the bluff body itself in order to disrupt the vortex formation [14]. Henning and King utilized distributed and steady blowing and suction along the trailing edge of a D-shaped elongated flat plate in order to disrupt the spanwise coherence of the vortex sheet [15]. Stalnov et al. used piezo-fluidic actuators in order to manipulate the stability of the shear layers in the case of a D-shaped body with a truncated trailing edge [16]. More recently several groups have reported the use of plasma actuators for the manipulation of the separation around cylinders and bluff bodies and eventual suppression of the vortex shedding [17–20]. Summarizing, several passive and active concepts exist for the control of vortex shedding. Both approaches present advantages and disadvantages regarding final applicability on industrial solutions. In general passive techniques are simple and robust yet their effectiveness is limited to very narrow operational conditions. On the other hand active techniques are more complex, require external power but they are more effective, flexible and adaptive to changes of operational conditions. A concept, which mitigates some of the drawbacks of active flow control techniques, is the use of plasma actuators. Plasma actuators present some favorable features for active flow control such as simple construction, robustness, low power consumption and high frequency response [21]. Early works have investigated the ability of plasma actuators to control leading edge separation on an airfoil operating at high angles of attack [22]. In case of vortex-dominated flows, Sung et al. [17] showed that a significant control of flow separation and wake formation around a circular cylinder can be achieved by plasma actuators placed at 90°, 120° and 150° angle from the forward stagnation point for Reynolds number in the order of 104. Thomas et al. [18] confirmed the suppression of the vortex street behind a circular cylinder in the same flow regime and also observed a significant reduction of acoustic noise. The plasma actuators kept the flow attached on the aft part of the cylinder, resulting in a merged jet of fluid on the wake centerline that suppressed the vortex shedding, reducing the near field sound pressure levels associated with shedding by 13 dB. Reviews on plasma actuators are published by Moreau [21], Corke et al. [23,24] followed by a recent overview of the state of the art actuators by Moreu and Benard [25]. Based on existing literature, plasma flow control for suppression of vortex shedding from D-shaped objects has received little effort. In this case, and in contrast to the circular cylinder scenario, the separation point is fixed at the edges of the truncated base and it is unlikely that flow control devices influence their position. The attention shifts therefore towards possible approaches to mitigate or suppress the vortex shedding mechanism by disruption of the communication between the shear layers and/or momentum addition in the recirculation area.

The goal of this study is to investigate the use of plasma actuators for the attenuation or suppression of vortex shedding from a D-shaped object. This is the initial step towards a plasma-based flow control system for truncated airfoils used on wind turbine blades. Although most engineering applications deal with airfoiltype objects typically in the turbulent flow regime, the current investigation is addressed to a simplified configuration of a flatplate with laminar boundary layer with the intention of addressing the fundamental mechanism of shedding control from a truncated object using plasma actuators. The objective is to describe the effects of plasma actuation in cases of several geometrical configurations in order to identify optimum approaches. Several diagnostic techniques are employed such as time resolved Particle Image Velocimetry (PIV) and Hot Wire Anemometry (HWA). These enable the quantitative visualization of the vorticity pattern in the Kármán wake and the spectral analysis of the flow velocity in the wake. Additionally, the velocity field obtained from PIV is submitted to modal decomposition. The POD approach is used as a quantitative approach to monitor the amount of fluctuating energy accumulated in the first two modes, which are known to be associated to the vortex street. Finally, the physical understanding of the operating mechanism of the identified best-performing actuator and a visualization of the induced velocity field is obtained with the transient technique, following the approach of Kotsonis et al. [26]. Section 2 of this paper presents a description of the experimental setup, actuators and measurement techniques. Section 3 presents results for the undisturbed flowfield, and actuation for vortex shedding suppression and actuation in quiescent conditions. Finally Section 4 provides discussion and conclusions. 2. Experimental setup 2.1. Flow facility The experiments are performed in a low-speed open jet wind tunnel at the Aerodynamics Laboratory of TU Delft. The exit section area is 0.40  0.40 m2. A flat plate of 300 mm length, and thickness h = 12 mm is immersed in a free-stream velocity ranging from 5 to 9.5 m/s. The plate employs an elliptical leading edge and a truncated trailing edge (Fig. 1). The Reynolds number range is 3800– 7300 based on the thickness of the base (12 mm). Turbulence intensity in the free-stream is approximately 0.5% at freestream velocities of 25 m/s. 2.2. Plasma actuator The dielectric barrier discharge (DBD) plasma actuator used in the current study belongs to a class of plasma actuators commonly used for the control of airflows at moderate velocity [21]. The actuator consists of two copper electrodes of 60 lm thickness and

Fig. 1. Shape and dimensions of the investigated D-shaped flat plate.

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10 mm width (12 mm for the covered electrode of the transverse configuration). The electrodes are separated by a dielectric layer, which consists of four layers of 2 mil (50.8 lm) thick polyimide Kapton foils. Total thickness of the dielectric layer is approximately 200 lm including adhesive. The actuator is installed on the aerodynamic surface as shown in Fig. 2. To be noted that the thickness of the electrodes and the dielectric layers is exaggerated for clarity and that the covered electrode is placed below the four dielectric layers. The exposed electrode is connected to the high voltage output of a TREK 20/20C voltage amplifier while the covered electrode is kept at ground potential. The high-voltage (HV) signal is alternating at a carrier frequency in the order of several kHz with a sinusoidal waveform. The resulting electric field exceeds the breakdown threshold for air and plasma is generated in a region close to the grounded electrode, where fast ionization, recombination and attachment (discharge) events occur [21]. The charged particles are subjected to Coulombian forces and accelerate in both upstream and downstream directions depending on their charge and the instantaneous value of the electric field. Momentum is transferred from the charged particles to neutral air particles through collisions. The phenomenon can be perceived and modeled macroscopically through a directional body force field exerted to the fluid surrounding the actuator. Due to the asymmetry in the placement of the electrodes and the existence of the dielectric layer, the body force induces a velocity field predominantly directed from the exposed to the covered electrode [27]. 2.2.1. Actuator configuration A range of 2D actuators configurations has been explored in this work in relation to their ability to suppress vortex shedding. The plasma actuators are placed on both sides of the flat plate at the trailing edge, either symmetrical or anti-symmetrical with respect to the wake centerline as illustrated in Fig. 3. Symmetric upstream plasma actuation (configuration 1) is intended to force transition of the boundary layer into turbulent state and destabilize the strong spanwise coherence of the Kármán vortices. The working principle behind the anti-symmetric actuation (configuration 2) configuration is to alter the strength of the vortices shed from the two sides and shift the ratio of their circulation outside of the range required for a stable vortex arrangement. According to existing studies [9] the latter range is given by 0.38 < C1/C2 < 2.62, where C1 and C2 represent the vortex strengths. Symmetric downstream plasma actuation (configuration 3) is proposed to energize the boundary layer close to the wall near the trailing edge with the intention to delay the interaction of the two shear layers and reduce the wake dimensions. Finally, a transverse actuator (configuration 4) is proposed, which is intended to act in the transverse direction with respect to the shear layers and to cut the circulation feeding during the vortex roll-up phase. This unconventional actuator configuration has been investigated marginally to this point [28]. The transverse plasma actuator consists of an electrode covered by a stack of dielectric layers located on the base of the truncated trailing edge. The exposed electrodes are mounted on the upper and lower surface of the flat plate at the trailing edge. This transverse configuration differs from traditional configuration in the sense that the covered electrode is perpendicular to the exposed electrode. It will be shown that the transverse configuration (Fig. 3)

Fig. 2. Schematic overview of a DBD plasma actuator.

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is the most efficient in vortex shedding suppression for the operational conditions investigated in this work. The actuators are operated using a sinusoidal peak-to-peak voltage Vpp of 18 kV, and carrier frequency facc of 2 kHz. Details of the power supply and control software can be found in Kotsonis et al. [26]. 2.3. Measurement techniques Hot Wire Anemometry and Particle Image Velocimetry are used to measure the flow velocity during the interaction of the plasma actuator with the wake flow as well as the flow solely induced by the transverse plasma actuator in a quiescent environment. 2.3.1. Hot Wire Anemometry The hot film anemometer, TSI Model 1201, is connected to a two-directional traversing system (accuracy 0.01 mm in both directions) to sample along stream-wise and wall-normal positions. Measurements are taken at normalized stream-wise location x/h = 1.25, 2.08 and 4.17 with y/h varying from 2.08 to 2.08 by steps of Dy/h = 0.208. Sampling rate is fixed at 10 kHz. In all cases measurement periods of two seconds are applied. The spectrum is evaluated using Welch’s algorithm by dividing the signal in 11 blocks overlapping by 50% with a frequency resolution of approximately 5 Hz. 2.3.2. Particle Image Velocimetry Particle Image Velocimetry is employed for characterizing the unperturbed vortex shedding wake as well as for studying the effect of the actuator. Additionally, in quiescent initial conditions a high-speed PIV system is utilized in order to capture the initial stages of the fluid acceleration, which are representative of the body force field induced by the actuator [26]. A 1 mm thick light sheet is generated by a Quantronix Darwin-Duo laser. The imaging system is composed of a LaVision HighSpeedStar CMOS cameras (1024  1024 pixels, 20 lm pixel pitch) equipped with a Nikon objective of 105 mm focal length plus a 40 mm extension tube and set at f# = 2.8. The imaging magnification factor is 0.51 resulting in a digital resolution of 26 pixels/mm. In such imaging conditions the diffraction limited particle image diameter is approximately 5 lm, which is far below a single pixel. The imaging focal plane is therefore slightly shifted from the illumination plane in order to defocus the particle images to a diameter of approximately 2 pixels. This expedient largely reduces the sub-pixel bias error known as peak-locking [29]. Acquisition is performed at 1 kHz with a 100 ls pulse separation time for the description of the transient flow regime. The time-averaged velocity field in the steady-state regime is obtained from measurements performed at 100 Hz during a period of 4 s. The PIV recordings are analyzed with the Davis 7.4 software from LaVision GmbH applying the iterative multi-grid image deformation technique [30]. The details of the image analysis are summarized in Table 1. The experiments conducted in the wind tunnel are arranged following the schematic representation of Fig. 4. The flat plate is installed at the middle position of the test section. The imaging system is composed of two cameras with imaging magnification of M1 = 0.23 (FOV1 = 88  88 mm2) and M2 = 0.54 (FOV2 = 38  38 mm2) respectively. The dual field of view (FOV) approach simultaneously returns an overall view of the wake and details of the flow in the vicinity of the trailing edge. Measurements performed at low frequency (10 Hz, 500 recordings) are used to evaluate the time-averaged velocity field and to decompose the fluctuations by POD. High-resolution details of the transient regime during the initial stages of actuation are obtained by double-frame recordings at 10 kHz with 50 ls pulse separation time, resulting in an effective 20 kHz recording rate.

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Fig. 3. A schematic overview of the investigated plasma actuator configurations and the coordinate system. Orange areas represent the electrodes and yellow areas separating the electrodes represents the dielectric layers. The arrows show qualitatively the plasma-induced flow in a quiescent environment. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Table 1 Settings for 2C-statistical analysis and 2C-TR PIV.

Set-up parameters for high repetition rate 2C-PIV Repetition rate Pulse separation time, Dt Objective focal length, f Aperture number, f# FOV Magnification, M Digital imaging resolution Interrogation window (IO) IO overlap Vector pitch Vectors per field Number of recordings

Quiescent air

Non-zero free-stream

Statistical/TR

Statistical

TR

Units

100/1000 80/100 145 2.8 40  40 0.51 25.6 32  32 50% 0.625 64  64 400/1000

10 100 60 4 88  88 0.23 11.6 16  16 50% 0.690 128  128 500

4000/10,000 100/50 145 2.8 88  88, 38  38/38  38 0.54 26.9 32  32 75% 0.297 128  128 1000/1500

Hz

ls mm – mm2 – pixel/mm pixel – mm – –

Fig. 4. PIV measurement setup in the wind tunnel.

3. Results In order to facilitate a clear understanding of the vortex shedding and suppression mechanisms, results are presented in a sequential manner closely following the experimental procedure. As such, results for the base, unperturbed flow are firstly presented. Next, the effect of plasma actuation on the vortex shedding

phenomenon is investigated for several geometrical configurations of the actuator. Special emphasis is given on the transverse plasma actuator since it is shown to have superior performance over the other tested configurations. Finally, measurements of the actuator-induced flow in quiescent conditions are presented in order to elucidate the features of the plasma forcing and provide an overall view of the working principles.

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3.1. Base flow

5

3.1.2. Wake characteristics An image of the instantaneous vorticity field with the typical Karman vortex shedding pattern is shown in Fig. 6 and the vortex shedding characteristic parameters are shown in Table 3. The primary frequency (f) of vortex shedding in combination with the free-stream velocity (U1) and the flat plate height (h) yields the Strouhal number, according to

St ¼

f h U1

The resulting Strouhal number is 0.216, which is in accordance with experimentally determined Strouhal numbers for bluff bodies by Akilli et al. [12], Thomas et al. [18], Jukes and Choi [19] and Thompson and Lotz [33]. The advection velocity of the vortex cores (0.54U1) is of the same order as the 0.6U1 for vortices in a laminar wake suggested by Lin and Hsieh [34] and the ratio of vortex transverse and stream-wise spacing is in agreement with the established value of 0.281 [35]. Table 2 Experimentally determined flow characterization parameters at 15 mm upstream of the trailing-edge. Symbol

Values

Parameter

unit

U1 Tu d99 d h Reh Reh H

5.0 0.5 4.71 1.47 0.62 3800 189.5 2.4

Free stream velocity Turbulence intensity Boundary layer thickness Displacement thickness Momentum thickness Trailing edge thickness Reynolds number Momentum thickness Reynolds number Shape factor

m/s % mm mm mm – – –

ulower

4 uupper

3

Blasius

y/δ*

3.1.1. Boundary layer characteristics Prior to any flow control effort a clear view on the base flow topology must be established. As mentioned earlier this work focuses on a laminar boundary layer. For freestream velocity of 5 m/s the boundary layer thickness at the trailing edge is 5 mm while displacement thickness d is 1.47 mm. The bluntness factor of the trailing-edge, B = h/d in the current experiments is 9, well above the limit of 0.3 typically considered as the critical value separating the regimes of sharp and blunt trailing-edge flows [31]. The flow parameters are summarized in Table 2. Particle Image Velocimetry (PIV) is employed to characterize the velocity profile within the boundary layer as well as the wake. The results demonstrate symmetry, as the two laminar boundary layers on the lower and upper sides shown in Fig. 5 are identical. The shape factor of the boundary layer near the trailing edge is approximately H = 2.4. The slight deviation from the Blasius value could be attributed to weak pressure gradients due to the open jet characteristics of the wind tunnel as well as unresolved areas near the wall due to light reflections. It should be noted here that the elevated freestream turbulence (0.5%) of the flow could affect the shedding characteristics compared to a respective cases of ‘‘cleaner’’ freestream conditions. Sohn and Reshotko [32] have demonstrated the existence of boundary layer receptivity mechanisms under conditions of high freestream turbulence which result in unsteady fluctuating modes in the boundary layer. Although the Reynolds number in this study (Reh = 3800) is significantly lower than the work of Sohn and Reshotko [32], the existence of these modes cannot be ruled out. It is nevertheless unlikely that this would have any effect on the operation or performance of the shedding suppression system as applied in this study.

2

1

0

0

0.5

1

/U Fig. 5. Boundary layer velocity profile from the lower surface (+) and the upper surface (o), x = 5 mm.

Fig. 6. Instantaneous vorticity field around the blunt trailing edge with U1 = 5 m/s. Black rectangle represents the trailing edge of the flat plate model.

Table 3 Vortex shedding parameters. Symbol

Parameter

Value

Unit

k T fshed Uconv a/b St

Wavelength Shedding period Shedding frequency Advection velocity Transverse/stream-wise spacing Strouhal number

29.8 11.1 90 2.68 0.29 0.216

mm ms Hz m/s – –

Time averaged velocity fields and the corresponding velocity fluctuations are shown in Fig. 7 for freestream velocity of 5 m/s. The separated region ends approximately two base heights downstream with the reattachment point placed on the symmetry axis. The maximum back-flow velocity of approximately 12% the free stream value is observed at x/h = 1.5. The spatial distribution of velocity fluctuations, indicate a constant inflow, confirming that the boundary layer prior to separation is laminar. The streamwise velocity component exhibits the highest level of fluctuations (u0 /U1 = 0.3) slightly upstream of the reattachment point. After vortex roll-up vigorous transverse motion is generated in between counter-rotating vortices, which confirms the high values of the vertical component fluctuations near the center of the wake in the range 2 < x/h < 4. 3.1.3. POD analysis In the laminar flow regime, the large-scale vortices are welldefined and dominate the overall fluctuations, allowing an efficient decomposition by proper orthogonal decomposition (POD) of the

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/U

/U

y/h

0

-2

0

2

4

0.2

2

0.1

y/h

1.2 1 0.8 0.6 0.4 0.2 0 -0.2

2

0

0

-0.1

-2

0

x/h

2

2

2

/U 0.5

2

/U 0.5

2

0.3

0

0.2

0.4

y/h

y/h

0.4

0.3

0

0.2

0.1

-2

0

2

-0.2

4

x/h

4

0

x/h

0.1

-2

0

2

4

0

x/h

Fig. 7. Time average velocity field and the fluctuations of the velocity field of the undisturbed flow; normalized stream-wise components (left) and transverse components (right). Black rectangle represents the flat plate model trailing edge. Unresolved regions are due to reflection and shadow (U1 = 5 m/s).

Karman wake [36]. This is performed using a set of 500 uncorrelated (measured at 10 Hz repetition rate) velocity field snapshots. The ‘method of snapshots’ [37] is adopted for the analysis of the velocity field. The individual contributions of the first three modes and the total averaged kinetic energy of the velocities fluctuations for the undisturbed flow are shown in Fig. 8, while the accumulative results are shown in Fig. 9. On the right vertical axis the accumulated contribution of the modes is plotted in percent while on the left axis the total averaged kinetic energy of the velocities fluctuations is shown. The total kinetic energy of the velocity fluctuations is determined by

Ekin ¼

NX v ectors i¼1

1 0 2 ððu Þ þ ðm0i Þ2 Þdxi dyi 2 i

where u0i and v 0i represent the fluctuating velocity components of the ith-velocity vector and dxi and dyi represent the vector spacing in x- and y-direction. The kinetic energy is normalized by dividing by the area of integration and the freestream velocity squared. The POD analysis shows that the flow field can be globally represented by the first two modes as the energy contained in the first two eigenmodes, E1+2, corresponding to the Von Kármán vortex

Fig. 9. Accumulated contribution of the eigenmodes to the total kinetic energy for the undisturbed flow with U1 = 5 m/s.

shedding phenomena, is 89.1% of the total kinetic energy. This is in accordance with previous experimental studies by Van Oudheusden et al. [38] and Gordeyev and Thomas [39].

3.2. Actuated flow

Fig. 8. Eigenmode contribution to the total kinetic energy for the undisturbed flow with U1 = 5 m/s. The eight eigenmodes presented here form 95% of the total kinetic energy.

3.2.1. Evaluation of actuator configuration To determine the performance of the plasma actuator configurations in vortex shedding suppression the POD technique is applied. The results of the POD analysis are presented in Table 4. Based on both the total kinetic energy and the individual mode it follows that the transverse plasma actuation system is the most effective. The individual contribution of the first two modes is halved and the total kinetic energy has diminished by approximately a factor 2.5. High potential in vortex shedding suppression is also observed by configuration 2, which generates contemporarily on one side a downstream-induced flow and on the other side an upstream-induced flow. Asymmetric actuation led to the destabilization of the alternate vortex shedding due to unequal strength of the vortices shed from both sides outside the range required for a stable vortex street presented previously. For conciseness in the current work only the most effective actuator, the transverse actuator, is further investigated. Description of the transient and steady behavior of the actuator is provided in the following sections.

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G. Nati et al. / Experimental Thermal and Fluid Science 46 (2013) 199–210 Table 4 POD results for the tested configurations. Plasma actuation with 18 kV peak-to-peak voltage at 2 kHz actuation frequency. Configuration

No plasma 1. Two upstream 2. One upstream, one downstream 3. Two downstream 4. Transverse

Energy contribution (%) 1st mode

2nd mode

3rd mode

47.0 33.9 30.7 39.1 23.3

42.1 23.0 23.5 34.4 17.9

1.6 6.0 6.9 3.6 7.2

3.2.2. Description of transient transverse actuation In this section the initial phase of the actuation is analyzed in the presence of free-stream velocity regarding the effect of the induced flow by the transverse system and its interaction with the shear layers and the recirculation region. Fig. 10 shows timeresolved development of the vorticity field for steady actuation at 18 kV peak-to-peak voltage with a 2 kHz carrier frequency. Prior to actuation a typical Von Kármán vortex shedding where the upper shear layer evolves into a vortex with negative vorticity (clockwise) and the lower shear layer into a vortex of positive vorticity (counter-clockwise) is observed at t = 0 ms of Fig. 10. Actuation of the system results in an induced flow normal to the shear layer (as demonstrated in quiescent conditions (Fig. 17)), with the effect of simultaneously deflecting the shear layer towards the wake centerline and redirecting part of the shear layer into a streamwise jet. The streamwise coherency of the shear layer after the start of actuation is reduced and it appears to form from smaller vortices. The instantaneous vorticity field also shows that near the trailing edge the flow is deflected to follow the base of the plate consequently narrowing the wake. As the induced flow moves along the base of the plate it encounters the induced flow originating from the opposing side at the plate center, where the two flows interact and merge into a single stream-wise jet. The jet generated along the wake centerline alters the wake by blocking the communication between the two shear layers. An additional effect of the jet is the creation of two large vortices on each side of the jet, as shown in Fig. 10 (t = 4.0 and t = 10 ms). These vortices are of opposite sign compared to the large vortices representing the vortex shedding process. The vortices induced by the jet interact with circulation in

Contribution of the 1st and 2nd mode (%)

Ekin/(A  U12) (103)

89.1 56.9 54.2 73.5 41.1

17.9 11.5 9.1 14.8 7.1

the shear layers, reduce the vorticity transfer from the shear layers to the recirculation region and thereby delay or prevent the growth of large and fully developed vortices. After the initial actuation, the induced jet of the transverse plasma actuators continues to interact with the shear layer and breaks down the wake into smaller structures (t = 14 ms and t = 25 ms). In a fully developed flow field after plasma actuation the near wake region behind the trailing edge becomes a turbulent region, as shown in Fig. 11. 3.2.3. Description of steady transverse actuation The time average velocity field and velocity fluctuations under continuous operation of the transverse plasma actuator are shown in Fig. 12. Significant differences can be observed compared to the undisturbed flow field shown in Fig. 7. The separated region has been reduced to a very small region (corresponding to the region with zero velocity in Fig. 12). Furthermore the large transverse velocities towards the wake centerline noted in the mean v component plot are slightly weakened and the regions show an elongated shape, indicating fewer coherent vortical structures, which are typical to the Karman shedding topology. The RMS plots of u and v show significant reduction of the fluctuations. The disappearance of the high intensity region of v fluctuations along the wake centerline demonstrates inhibition of the roll up process of vertical structures across the wake centerline. The alteration of the wake is confirmed by the POD results. The individual mode contributions for both the undisturbed flow field and the case with plasma actuation are shown in Fig. 13, while the accumulative results are shown in Fig. 14. The POD analysis shows that the transverse plasma actuator significantly reduces the contribution of the first two eigenmodes

Fig. 10. The start-up sequence of a transverse plasma actuation system showing the vorticity field. Images are acquired at 10 kHz sampling frequency. The black rectangle represents the model trailing edge (U1 = 5 m/s).

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Fig. 11. Instantaneous vorticity field with U1 = 5 m/s for (a) no plasma and (b) 18 kV steady plasma actuation. The black rectangle represents the model surface and unresolved areas.

0

-2 0

2

4

/U 1.2 1 0.8 0.6 0.4 0.2 0 -0.2

/U 0.2

2

0.1

y/h

y/h

2

0

0

-0.1 -2

0

2

x/h 2

2

/U 0.5

2

/U 0.5

2

0.3

0

0.2

0.4

y/h

y/h

0.4

0.3

0

0.2

0.1 -2 0

2

-0.2

4

x/h

4

0

x/h

0.1 -2

0

2

4

0

x/h

Fig. 12. Average velocity field and fluctuations of the velocity field with transverse plasma actuation; normalized stream-wise components (left) and transverse components (right). Black rectangle represents the flat plate model trailing edge. Unresolved regions are due to reflection and shadow (U1 = 5 m/s).

Fig. 13. Eigenmode contribution to the total kinetic energy for the case without plasma actuation (solid) and with 18 kVpp and facc = 2 kHz transverse plasma actuation (dotted). The eigenmodes presented represent 95% of the total kinetic energy (U1 = 5 m/s).

(corresponding to the Von Kármán vortex shedding phenomena) to the total kinetic energy, from 89.1% to 37.8%. Moreover, the contribution of the third mode to the total kinetic energy has increased from 1.6% to 9.0%. This indicates that in case of transverse plasma

Fig. 14. Accumulated contribution of the eigenmodes to the total kinetic energy for the case without plasma actuation (solid) and with 18 kVpp and facc = 2 kHz transverse plasma actuation (dotted). The eigenmodes presented represent 95% of the total kinetic energy (U1 = 5 m/s).

actuation a wake consisting of smaller vortical structures is generated, which is confirmed by the instantaneous image of the wake shown previously in Fig. 11. Taking the total kinetic energy of the fluctuating components into account the transverse plasma actuation reduces it by approximately 60% compared to the case without plasma actuation.

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HWA measurements are also employed in order to extract the frequency spectrum from both the actuated and non-actuated cases. Spectral analysis confirms the POD results indicating an attenuation of the frequency peak corresponding to the large scale Von Kármán vortices (Fig. 15). For the case without plasma actuation a peak can be seen at the shedding frequency (90 Hz). After transverse plasma actuation the peak is reduced showing the suppression of the Kármán wake. To obtain the energy associated with the Kármán wake vortices, the power spectral density is numerically integrated from 79 to 109 Hz resulting in a reduction of the near-field sound pressure level by plasma actuation of 10 dB.

Fig. 15. Frequency spectrum at x/h = 2.08 and y/h = 0.625 (where the origin is the center of the trailing edge) for no plasma (solid) and transverse plasma actuation (dashed) (U1 = 5 m/s).

3.2.4. Performance of actuation for varying freestream velocities In order to further investigate the potential of a transverse actuation system the free-stream velocity is increased to 7 and 9.5 m/s (respectively Reh  5300 and 7300). For each velocity under investigation the kinetic energy distribution over the specific modes and the total kinetic energy are determined for both cases with and without plasma actuation and are provided in Table 5. For ease of comparison the results obtained during the experiments for 5 m/s free-stream velocity are also presented.

Table 5 POD results for varying free-stream velocities for cases with and without plasma actuation. Plasma actuation with 18 kV peak-to-peak voltage at 2 kHz actuation frequency. U1 (m/s)

Actuation

Energy contribution (%) 1st mode

2nd mode

3rd mode

Contribution of 1st and 2nd mode (%)

Ekin/(A  U12) (103)

5

No plasma 18 kV, 2 kHz

45.0 23.3

43.1 17.9

1.8 7.2

88.1 41.1

17.9 7.1

7

No plasma 18 kV, 2 kHz

44.6 27.1

43.0 23.2

2.2 5.8

87.6 50.3

18.6 6.5

9.5

No plasma 18 kV, 2 kHz

45.1 43.6

41.3 35.3

2.2 2.8

86.4 78.9

16.3 10.1

Fig. 16. Vorticity field, for (a) U1 = 7 m/s without plasma actuation, (b) U1 = 7 m/s with 18 kV plasma actuation, (c) U1 = 9.5 m/s without plasma actuation and (d) U1 = 9.5 m/s with 18 kV plasma actuation. The black rectangle represents the model surface and unresolved areas.

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Fig. 17. Start-up sequence of a transverse plasma actuation system with 18 kV peak-to-peak voltage and 2 kHz actuation frequency (time values indicate elapsed time from the start of actuation).

Fig. 18. Instantaneous images showing the velocity field (left) and the vorticity field (right) resulting from transverse plasma actuation. Actuation peak-to-peak voltage is 18 kV at 2 kHz actuation frequency. The black rectangle represents the flat plate model.

For free-stream velocity of 7 m/s similar results are obtained as for the discussed 5 m/s free-stream velocity case. The contribution to the total kinetic energy by the first two modes has increased to over 50% and the total kinetic energy is reduced by a factor 3. As the free-stream velocity increases to 9.5 m/s the limitations of the current plasma actuation system are evident. The energy distribution over these two modes is very similar for both cases, with and without plasma actuation. The kinetic energy contained in the wake is however halved under plasma actuation, showing that at 9.5 m/s although the transverse actuator is not capable to suppress the vortex shedding, it is able to attenuate its strength. This can be seen in Fig. 16. 3.3. Characterization of transverse actuation in quiescent conditions In order to further clarify the working mechanisms of the transverse actuator, high-speed PIV measurements are employed in quiescent conditions similar to previous characterization studies by the authors [26]. The time sequence of the velocity field in the initial phase of the actuation is presented in Fig. 17 (time values indicate elapsed time from the start of actuation). Shortly after actuation begin contribution of the pressure gradient and of the

viscous effects to the momentum budget are negligible with respect to the leading terms represented by the fluid acceleration and the body force distribution causing it. In the initial linear regime of constant acceleration (Fig. 17, t = 2 ms), the instantaneous velocity field represents the distribution of the body force [26]. Within the first millisecond, the fluid accelerates from the edges of the plate towards the mid-section, inducing two small opposing wall jets of approximately 1 mm thickness. Up to this point the system follows the behavior of two independent DBDs. At t = 4 ms the two jets interact producing a stagnation region close to the wall from which a wall normal jet emerges. The latter gains momentum later (t = 10 ms) and penetrates further downstream accompanied by a starting vortex pattern. In the steady-state regime, the jet is fully developed and shows an unsteady behavior that resembles that of transitional jets. Considering the characteristic jet diameter and velocity the Reynolds number does not exceed 500, which should not result into any transition to turbulence. The irregular fluctuations indicate the unstable interaction between the two opposing jets at the stagnation point close to the wall. An instantaneous snapshot of the fully developed flow field is shown in Fig. 18 and the time averaged flow field in the steady-state regime is presented in Fig. 19.

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209

Fig. 19. Average flow field in m/s resulting from still air initial conditions; stream-wise velocity (left) and transverse velocity (right). Actuation peak-to-peak voltage is 18 kV at 2 kHz actuation frequency. The black rectangle represents the flat plate model.

The results indicate that two equal wall jets are accelerated by the actuator from both the upper and lower edges over the covered electrode. These two streams interact at the mid-section of the plate generating a stagnation point and a continuous stream-wise jet normal to the base of the plate. The results show an averaged velocity field with maximum velocities of 3 m/s both in the regions above the covered electrode as well as in the generated jet. The formation of a wall normal jet by plasma actuation has been proposed earlier by [40] and [41] creating a plane micro-jet by two opposing linear DBD actuators and more recently by [42] who created a steady jet using only one actuator. Those results were however obtained with parallel facing electrodes, while in the current case the actuator is configured with a single covered electrode that interacts with two exposed electrodes perpendicular to it.

4. Conclusions The current work investigates the potential of plasma actuators in suppression of vortex shedding from a truncated trailing edge of a D-shaped elongated flat plate using plasma actuators. A configuration of plasma actuators introduced as ‘‘transverse actuation’’ is developed in which the covered electrode is placed perpendicular to the free-stream direction at the base of the trailing edge. The working principle of a transverse system has been analyzed in both quiescent and in the presence of free-steam velocities of 5, 7 and 9.5 m/s. The induced flow by the transverse actuator is parallel to the base of the trailing edge originating from both the upper and lower corners. These wall jets further merge into a single stream-wise jet along the wake centerline. The induced flow of the actuators appears to act at two regions (a) at the corners of the trailing edge where separation occurs and (b) along the wake centerline. At the corners of the trailing-edge the actuators deflect the shear layer towards the wake centerline and also breaks it into smaller vortices. The induced streamwise jet acts to block the interaction of the two shear layers and consequently cutting-off a part of the circulation feeding. The POD analysis showed that the total kinetic energy contained in the fluctuating components of the velocity field is reduced by approximately 60% while the energy contained in the corresponding Von Kármán modes is reduced by a factor 6. Hotwire measurements show that the corresponding vortex shedding frequency peak is reduced during steady plasma actuation by 10 dB. The actuator has proven its effectiveness in vortex shedding suppression for free-stream velocities up to 7 m/s (Reh = 5300). At higher velocities the Von Kármán vortex shedding is not suppressed.

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