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.

Analytical results for pitching kinematics and propulsion performance of flexible foil

“…Natural flyers and swimmers employ the complex interaction between the foils and the surrounding fluid to generate sufficient thrust to locomotion, where the deformation of the flexible foil adds new challenges to the flow-structure interaction. Thus, a vast number of investigations from various aspects have been deployed to reveal the mechanism of the interaction between the flexible foil and the fluid, such as from active and passive foil deformation (Tytell et al 2010;Flammang & Lauder 2013;Ulrich & Peters 2014;Joshi & Bhattacharya 2022), from localized and distributed flexibility (Shahzad et al 2018;Shi, Xiao & Zhu 2020;Wang, Huang & Lu 2020;Kurt, Mivehchi & Moored 2021;Wang et al 2021;Demirer et al 2022), from tethered and unconstrained motion (Arora et al 2018;Lin, Wu & Zhang 2020;Fernandez-Feria, Sanmiguel-Rojas & Lopez-Tello 2022;Wu et al 2022) and from vortical structures and their interactions (Eldredge & Jones 2019;Linehan & Mohseni 2020;Jia et al 2021;Zhang et al 2021;Verma & Hemmati 2022). Among these investigations, elucidating the propulsive performance of the flexible foil earns much attention as this will not only help to unveil the flight or swimming mechanism (Wu 2011;Gazzola, Argentina & Mahadevan 2014;Sun 2014;Lauder 2015;Chin & Lentink 2016;Saadat et al 2017;Dabiri 2019;Wang et al 2022), it will also help to optimize the manmade flying vehicles and swimming robotics through flapping propulsion (Karasek et al 2018;Zhu et al 2019;Chin et al 2020;Haider et al 2021;Lee, Kim & Chu 2021;…”

“…Thus, a vast number of investigations from various aspects have been deployed to reveal the mechanism of the interaction between the flexible foil and the fluid, such as from active and passive foil deformation (Tytell et al . 2010; Flammang & Lauder 2013; Ulrich & Peters 2014; Joshi & Bhattacharya 2022), from localized and distributed flexibility (Shahzad et al . 2018; Shi, Xiao & Zhu 2020; Wang, Huang & Lu 2020; Kurt, Mivehchi & Moored 2021; Wang et al .…”

Analysis of Shear Stress on Flow around Sudden Accelerated Plate (Stokes’ First Problem)

“…It significantly contributes to our understanding of boundary layer development, the establishment of velocity profiles, and the emergence of flow instabilities. Through meticulous analysis, experimental, and numerical simulations, researchers have gained a deeper appreciation of the complexities inherent in fluid flows and the pivotal role played by fundamental principles in elucidating these phenomena (Grift et al, 2019;Joshi & Bhattacharya, 2022).…”

A Study on Influence of Flapping Dynamic Characteristics on Vibration Control of Active Rotor with Trailing-Edge Flaps

“…Additionally, the dynamic twist technique has other applications. A series of studies on the effect of dynamic twisting on the flow field and the unsteady forces were conducted by Bhattacharya et al [7][8][9]. However, the active twist rotor has not been used in engineering applications due to the limitations in drive technology.…”