A high-fidelity numerical study on the propulsive performance of pitching flexible plates

Abstract

In this paper, we numerically investigate the propulsive performance of three-dimensional pitching flexible plates with varying flexibility and trailing edge shapes. We employ our recently developed body-conforming fluid-structure interaction solver for our high-fidelity numerical study. To eliminate the effect of other geometric parameters, only the trailing edge angle is varied from 45° (concave plate), 90° (rectangular plate) to 135° (convex plate) while maintaining the constant area of the flexible plate. For a wide range of flexibility, three distinctive flapping motion regimes are classified based on the variation of the flapping dynamics: (i) low bending stiffness KBlow, (ii) moderate bending stiffness KBmoderate near resonance, and (iii) high bending stiffness KBhigh. We examine the impact of the frequency ratio f* defined as the ratio of the natural frequency of the flexible plate to the actuated pitching frequency. Through our numerical simulations, we find that the global maximum mean thrust occurs near f*≈1 corresponding to the resonance condition. However, the optimal propulsive efficiency is achieved around f* = 1.54 instead of the resonance condition. While the convex plate with low and high bending stiffness values shows the best performance, the rectangular plate with moderate KBmoderate is the most efficient propulsion configuration. To examine the flow features and the correlated structural motions, we employ the sparsity-promoting dynamic mode decomposition. We find that the passive deformation induced by the flexibility effect can help in redistributing the pressure gradient, thus, improving the efficiency and the thrust production. A momentum-based thrust evaluation approach is adopted to link the temporal and spatial evolution of the vortical structures with the time-dependent thrust. When the vortices detach from the trailing edge, the instantaneous thrust shows the largest values due to the strong momentum change and convection process. Moderate flexibility and convex shape help to transfer momentum to the fluid, thereby improving the thrust generation and promoting the transition from drag to thrust. The increase in the trailing edge angle can broaden the range of flexibility that produces positive mean thrust. The role of added mass effect on the thrust generation is quantified for different pitching plates and the bending stiffness. These findings are of great significance to the optimal design of propulsion systems with flexible wings.