Vortex structures and vortical formation in flapping flight are directly related to the force production. To analyze the connection between vortex structures and aerodynamic performance of flapping flight, we have developed highly efficient algorithms for large-scale flow simulations with moving and deforming bodies. To further understand the underlying mechanisms of force generation caused by the coherent structures of the vortex formation, a new analysis method has been developed to measure the influence of Proper Orthogonal Decomposition (POD) modes on aerodynamic forces.
It is challenging to finish three-dimensional Direct Numerical Simulations (DNS) of insect flight in a limited amount of time. In the current work, the Modified Strongly Implicit Procedure (MSIP) has been implemented into an existing Computational Fluid Dynamics (CFD) solver, as a smoother for the multigrid method to solve the pressure equation and an iterative method to solve the momentum equation. The new solver is capable of performing a 17-million-mesh simulation within 10 days on a single core of an Intel i5-3570 chip at 3.4GHz, nearly 10 times faster than the traditional Line-SOR solver.
Based on this numerical tool, the free flight of a dragonfly for eight-and-a-half wing beats is studied in detail. The results show that the dragonfly has experienced two flight stages during the flight. In a maneuver stage, wing-wake interaction generated by the fore- and hindwings attenuates the total force by 8% (peak value). In contrast, in an escape stage, the fore- and hindwings collaborate to generate force which is 8% larger than when they flap separately. Especially, the peak force on the forewing is significantly increased by 42% in a downstroke and this enhancement is known to associate with a distorted trailing edge vortex, as demonstrated by a theoretical model based on wake survey methods. The movement of the trailing edge vortex is a response to the motion of the hindwing. When the fore- and hingwings flap closely with only a short distance existing between them, the hindwing exerts a wall effect to the trailing edge vortex.
Vortex formation of flapping flight and force generation are considered to be closely linked; however, it is difficult to accurately determine the influence of an individual vortex on the overall aerodynamic performance. Here, as an alternative, we examine the influence of coherent structures, which are thought as special types of vortices in terms of kinetic energy. First, wake structures are decomposed by the POD method and the most energetic vortices are extracted. Then, a pressure corrected POD Reduced-Order Models (ROM) method is used to verify that the POD modes can capture the dynamics of the flows. Finally, the force of POD modes is quantified by a new method, termed the POD mode Force Survey Method (POD-FSM).
The process is applied to investigate the flow field generated by a two- or three-dimensional plate undergoing a pitching-plunging motion. Superposition of force of the POD modes shows a good agreement with the DNS result. In addition, it is found that some POD modes have zero lift, and some have zero thrust. These force behaviors are related to symmetry of POD mode. According to the symmetry or antisymmetry about the streamwise line (or the crossflow plane in three-dimension), the POD modes can be qualitatively grouped into two sets. Combining POD modes in the same set can help to decompose the flow into thrust- and lift-producing flows. It is found that the force acting on the plate is a linear combination of the force of the thrust- and lift-producing flows and their interactions. Because two flows have different frequency spectrum, it is possible to perform flow control with respect to frequency to achieve the desired aerodynamic performance.