Active control of vortex shedding from a blunt trailing edge using oscillating piezoelectric flaps

Piezoelectric bending actuators have been used to drive flaps to manipulate vortex shedding from a nominally two-dimensional blunt trailing edge (BTE) using three different actuation methods. The experiments were conducted in a wind tunnel at a Reynolds number of $\text{Re}\left(h\right)=2600$ where $h$ is the height of the BTE. A combination of base-pressure measurements at the BTE and high-speed particle image velocimetry was used to characterize actuator performance over their operating range. Proper orthogonal decomposition was also applied to study the energy content of the primary vortex shedding structures in the wake during actuation. Cases of significant vortex shedding amplification and suppression were investigated. Vortex shedding amplification occurred when the frequency of actuation matched that of the natural wake process, resulting in the turbulent kinetic energy associated with two-dimensional vortex shedding increasing from 70% to 90%. This led to higher turbulence intensities, a shortened recirculation region, and more organized vortex shedding in general. Vortex shedding suppression was caused by the generation of small spanwise vortices at the tips of the actuators, which disrupted the interaction between the separating shear layers. The energy associated with vortex shedding was reduced from 70% to 20% in this case, resulting in a significant attenuation of the shedding pattern for at least six BTE thicknesses downstream. Vortex shedding suppression was accompanied by greatly reduced turbulence intensities, a narrowed wake, and a lengthened recirculation region. The actuators were also capable of forcing symmetry in the near-wake using a symmetric actuation method, but the vortex shedding resumed downstream, although with a reduced frequency. Finally, an adaptive slope-seeking controller was designed using the base-pressure measurements at the BTE in real time. The closed-loop controller was capable of seeking and maintaining an optimal input for vortex shedding suppression, even during slow variations in freestream velocity.

Figure 1

Schematic of the experiment and sectional view of the modified BTE. Note that the $z$ coordinate runs in the spanwise direction with $z=0$ located at center span.

Figure 2

Frequency response of the piezoelectric flap construction. The tip displacement ($d_{\mathrm{tip}}$) was measured using a calibrated high-speed camera with a resolution of $22.4\mu \mathrm{m}/\mathrm{pix}$, and the piezoelectric flap was driven using a sinusoid of maximum amplitude ($\pm 30$ V).

Figure 3

Schematic representation of the symmetric, asymmetric, and single actuation methods. Note that $T_a$ is the period of actuation.

Figure 4

Power spectral density (PSD) of $P^{\prime }$ at $\text{Re}\left(h\right)=2600$ for symmetric actuation at 30 Hz. The plot indicates that the pressure fluctuations caused by vortex shedding and the acoustic actuation noise are the only significant contributors to the microphone signal.

Figure 5

Left: Schematic representation of how the dither signal $ad\left(t\right)$ provides a measure of the slope of the steady-state map, which is proportional to the magnitude of the output oscillations; schematic adapted from Becker et al. [55]. Right: The control loop structure implemented here for adaptive slope seeking.

Figure 6

Contour plots of the suppression variable [$\sigma$; see Eq. (1)] over the entire operating envelope for (a) symmetric, (b) asymmetric, and (c) single actuation. Solid lines denote negative contours, and dashed lines denote positive contours. The hatched section centered at $f_u$ represents an area of no data, as $\sigma$ cannot be evaluated near the unforced wake frequency. Note that $V_{max}=30$ V and $f_{max}=180$ Hz.

Figure 7

Energy content within the first two POD modes used to identify the strength of the primary vortex shedding instability. Maximum vortex shedding suppression occurs at $f_a=3f_u$ for symmetric and asymmetric actuation and at $f_a=3.5f_u$ for single actuation. Cases of vortex shedding amplification are visible at $f_a=f_u$ and $2f_u$.

Figure 8

(a) Mean streamwise velocity contours $\langle U\rangle$, (b) streamwise turbulence intensities $\langle u^2\rangle$, (c) transverse turbulence intensities $\langle v^2\rangle$, and (d) instantaneous snapshots of vorticity ${\omega }_z$ for the unforced and amplified wakes. Time-resolved videos of the structures in panel (d) are available in Movie 1 [65].

Figure 9

Phase plots of the first two POD mode amplitudes ($a_i\left(t\right)$) normalized by the corresponding eigenvalues (${\lambda }_i$) and compared to those of the unforced flow for (a) symmetric and (b) asymmetric amplification. A normalized phase plot that more closely resembles the unit circle is indicative of more coherent vortex shedding.

Figure 10

Schematic of the development of the near-wake vortices relative to the piezoelectric flap movement during asymmetric vortex shedding amplification.

Figure 11

(a) Mean streamwise velocity contours $\langle U\rangle$, (b) streamwise turbulence intensities $\langle u^2\rangle$, (c) transverse turbulence intensities $\langle v^2\rangle$, and (d) instantaneous snapshots of vorticity ${\omega }_z$ for the symmetric, asymmetric, and single actuation suppression cases. Time-resolved videos of the structures in panel (d) are available in Movie 2 [65].

Figure 12

Power spectral density (PSD) of the fluctuating component of streamwise velocity ($u$) as a function of distance from the BTE (evaluated at $y=h$) for the unforced wake and for (a) symmetric and (b) single actuation. Complete removal of the vortex shedding frequency occurs as far as $x=6h$ downstream during symmetric actuation at $f_a=3f_u$.

Figure 13

(a) Mean streamwise velocity contours $\langle U\rangle$, (b) streamwise turbulence intensities $\langle u^2\rangle$, (c) transverse turbulence intensities $\langle v^2\rangle$, and (d) instantaneous snapshots of vorticity ${\omega }_z$ for symmetric actuation at $f_a=1.5f_u$. Time-resolved videos of the structures in panel (d) are available in Movie 3 [65].

Figure 14

Power spectral density (PSD) of the fluctuating component of streamwise velocity ($u$) as a function of distance from the BTE (evaluated at $y=h$) for the unforced wake and for symmetric actuation at $f_a=1.5f_u$. The dominant wake frequency shifts to a value of $0.75f_u$ during actuation.

Figure 15

Schematic of the instantaneous wake structure resulting from symmetric actuation at $f_a=1.5f_u$. Actuation forces the simultaneous roll-up of shear layers at the trailing edge. The resulting symmetric vortex pair quickly destabilizes and moves to one side of the wake or the other in an alternating fashion to form a shedding pattern at a reduced frequency of $0.75f_u$. The vortex pairs break into smaller concentrations of vorticity as they convect downstream.

Figure 16

The plateau-style steady-state maps for the current application of adaptive slope seeking. The optimal actuation frequency according to these maps is $f_a/f_u=2.4$, and the map appears static within $2600\le \text{Re}\left(h\right)\le 3500$.

Figure 17

System response of the adaptive slope-seeking controller at $\text{Re}\left(h\right)=2600$. The controller seeks the optimal input of $f_a/f_u=2.4$ in approximately 30 sec and maintains this value over time. The values for $P_{\mathrm{rms}}^{\prime \prime }$ during control have been normalized by the rms of the filtered pressure fluctuations in the unforced wake ($P_{u,\mathrm{rms}}^{\prime \prime }$). In the lower plot, the gray line represents the true signal, and the black line is a moving average of the signal that has been added to better show the trend.

Figure 18

System response to a simulated disturbance in the form of an unknown change in freestream velocity. The slope-seeking controller is able to reject the change in freestream velocity and eventually return to the optimal input of $f_a/f_u=2.4$. The values for $f_a/f_u$ were determined by using the mean of the square wave $f_a$. The gray line in the lower plot represents the true signal, and the black line is a moving average that has been added to better show the trend. $P_{\mathrm{rms}}^{\prime \prime }$ was normalized using the rms of the filtered pressure fluctuations in the unforced wake at $\text{Re}\left(h\right)=2600$.

Figure 19

Power spectral density (PSD) of the first six POD mode amplitudes $a_i\left(t\right)$ for (a) the unforced wake and (b) the wake suppressed by symmetric actuation at $f_a=3f_u$.