Flow around a Flat Plate in Shallow and Deep Stall at Re = 6 x 104

Figure 3.33 shows dye flow visualization, й1/ЦХ!, and m3/(U^/c) contours from Kang et al. [324] for the flow about a flat plate in shallow stall at Re = 6 x 104. They gave the shallow stall kinematics as

h(t/T) = h0cm cos(2nt/T), (3-19)

where h(t/T) is the location of the center of rotation (xp/cm = 0.25) of the airfoil measured normal to the free-stream, h0 = 0.5 is the normalized amplitude of the plunge motion, a(t/T) is the geometrical AoA measured relative to the incoming free – stream with velocity UTO, a0 = 8° is the mean AoA, p = 90° is the phase lag between the pitching and plunging motion, and aa = 8.43° is the amplitude of the pitching motion. The resulting non-dimensional numbers are к = 0.25 and St = 0.08.

As shown in Figure 3.33, leading-edge separation is observed over the majority of the motion cycle. At the top of the downstroke (t/T = 0.00) the boundary layer separates at the leading edge and reattaches before the half-chord, forming a thin shear layer that covers the suction side of the flat plate. As the flat plate plunges down, the effective AoA increases, reaching its maximum at t/T = 0.25. During this portion of the downstroke, the flow field shows flow separation at the leading edge, which produces a closed recirculation region and formation of an LEV capturing the vorticity shed at the leading edge. The LEV is observed during most of the downstroke, convecting downstream, until it eventually detaches from the flat plate at the bottom of the downstroke, t/T = 0.50. A TEV forms at t/T = 0.33, 0.42, and 0.50 due to the interaction of the LEV and the trailing edge. During the upstroke the boundary layer reattaches.

The increase in the induced AoA due to the plunging motion is not compensated by the delayed pitch in the deep stall case where aa = 0° in Eq. (3.20). The flow field is characterized by separated flow throughout the downstroke, consistent with the more aggressive time history of effective AoA [323]. This vortical structure serves as a mechanism to enhance lift by its lower pressure region in the core. Figure 3.34 shows the dye flow visualization, щ/Um, and m3/(U^/c) contours at Re = 6 x 104 from Kang et al. [324]. The LEV is stronger and separates at earlier time instants compared to the shallow stall case. As the flat plate plunges toward the bottom of the downstroke, a well-defined TEV forms at the trailing edge of the flat plate.