The unsteady force response of an accelerating flat plate with controlled spanwise bending

Abstract

The unsteady force response of an accelerating flat plate, subjected to controlled spanwise bending, is investigated experimentally. The flat plate was held normal to the flow (at an angle of attack of $90^{\circ }$ ), and it was dynamically bent along the spanwise direction with the help of internal actuation. Two bending directions were tested. In one case, part of the plate (denoted by flexion ratio) was bent into the incoming flow (the bend-down configuration). In another case, the plate was bent away from the flow (the bend-up configuration). We used two different aspect ratio ( $AR$ ) plates, namely $AR = 2$ and 3. Three acceleration numbers, namely $A_c = 0.57$ , 1.6 and 3.2 (corresponding to dimensional acceleration of 0.036, 0.1 and 0.2 m s $^{-2}$ , respectively) were tested with a fixed terminal Reynolds number (Re) of 18 000. For each acceleration number, three bending durations, namely 1.2, 2.4 and 3.6 s were implemented. The results indicate that the highest impulse was imparted by the highest bending rate (duration 1.2 s) during all three accelerations tested. We show that controlled spanwise bending can significantly change the unsteady force response by manipulating the inertial forces during a start-up manoeuvre. The unsteady forces depend on the vector sum of the forward acceleration and the bending acceleration of the plate. The unsteady drag was augmented when the plate was bent towards the incoming flow. The initial force peaks were significantly reduced when the bending direction was reversed. The development of the edge vortices from the flat plate was measured with the help of particle image velocimetry (PIV) at the 70 % and the 90 % span locations. The PIV measurements were also carried out at the midchord plane closer to the tip region to capture the growth of the tip vortex. The vorticity field calculated from these PIV measurements revealed that controlled bending contributed to a variation in the circulation growth of the edge vortices. During the bend-down case, the circulation growth was faster and the tip vortices stayed closer to the plate. This resulted in increased interaction with the edge vortex at the 90 % span. This interaction was more severe for $AR = 2$ . During the bend-up case, the growth of the edge vortex was delayed, but the vortex grew for a longer time compared with the bend-down case. Finally, a mathematical model is presented which correctly captured the trend of the force histories measured experimentally during both the bend-up and bend-down cases.