Active flow control for drag reduction of a plunging airfoil under deep dynamic stall

High-fidelity simulations are performed to study active flow control techniques for alleviating deep dynamic stall of an SD7003 airfoil in plunging motion. The flow Reynolds number is $\text{Re}=60000$ and the freestream Mach number is $\text{M}=0.1$. Numerical simulations are performed with a finite-difference-based solver that incorporates high-order compact schemes for differentiation, interpolation, and filtering on a staggered grid. A mesh convergence study is conducted and results show good agreement with available data in terms of aerodynamic coefficients. Different spanwise arrangements of actuators are implemented to simulate blowing and suction at the airfoil leading edge. We observe that, for a specific frequency range of actuation, mean drag and drag fluctuations are substantially reduced while mean lift is maintained almost unaffected, especially for a two-dimensional (2D) actuator setup. For this frequency range, 2D flow actuation disrupts the formation of the dynamic stall vortex, which leads to drag reduction due to a pressure increase along the airfoil suction side, towards the trailing edge region. At the same time, pressure is reduced on the suction side near the leading edge, increasing lift and further reducing drag.

Figure 1

Actuator setup: (a) actuator location in the $x-y$ plane and (b) 3D view of the 2D actuator.

Figure 2

Profiles of the function $P\left(z\right)$ that specifies the spanwise arrangement of actuation.

Figure 3

Grids considered in the mesh refinement study (only every other grid point in the $x-y$ plane is shown here).

Figure 4

Aerodynamic coefficients obtained using grids 1 and 2 and from Ref. [12] as a function of the effective angle of attack $\alpha$.

Figure 5

Cycle to cycle variations in aerodynamic coefficients (grid 1).

Figure 6

Airfoil position for different phase angles $\varphi$.

Figure 7

Spanwise-averaged vorticity contours at different phases of the plunging motion without actuation (see also the Supplemental Material [48]).

Figure 8

Isosurfaces of the $Q$ criterion colored by $C_P$ at different phases of the plunge motion without actuation.

Figure 9

Variations in aerodynamic coefficients for different actuation frequencies St and coefficient of momentum $C_{\mu }$ for 2D actuated flows. We refer to simulations with different $C_{\mu }$ as case 1, 2, or 3.

Figure 10

Mean aerodynamic loads compared to the baseline flow, mean lift to mean drag ratio, and aerodynamic damping using 2D actuation.

Figure 11

Aerodynamic coefficients versus effective angle of attack for 2D actuated flows with different frequencies (case 2).

Figure 12

Pressure coefficient $C_P$ contours with isolines of $z$ vorticity for spanwise-averaged flows with 2D actuation (case 2).

Figure 13

Comparison between span-averaged values of $C_P$ for 2D actuators with different frequencies (case 2). The vertical dashed line indicates the location of $x_{\text{vsn}}$.

Figure 14

Position $x_{\text{vsn}}$ where the inward pointing surface normal at the suction side is vertical.

Figure 15

Comparison of $C_P$ between baseline and 2D actuated flow with $\text{St}=5$.

Figure 16

Comparison of $C_f$ between baseline and 2D actuated flow with $\text{St}=5$.

Figure 17

Spanwise-averaged vorticity contours at different phase angles for the $\text{St}=5$ controlled case (case 2).

Figure 18

Comparison of aerodynamic coefficients obtained by 2D and 3D actuation with $\text{St}=5$ (case 2).

Figure 19

The $Q$ criterion colored by $C_P$ comparing 2D and 3D actuation with $\text{St}=5$ (case 2) at various phases of the plunge motion.

Figure 20

Distribution of $C_P$ over the airfoil suction side (flow is directed from left to right) for 2D and 3D actuation with $\text{St}=5$ (case 2).

Figure 21

Distribution of $C_f$ over the airfoil suction side (flow is directed from left to right) for baseline and 2D and 3D actuation with $\text{St}=5$ (case 2).

Figure 22

Spanwise-averaged values of $C_P$ for different configurations of actuation with $\text{St}=5$ (case 2). The vertical dashed line indicates the location of $x_{\text{vsn}}$.