The special aerodynamic characteristics of insects have attracted the interest of biologists and engineers. In this paper, aerodynamic modeling methods for flapping flight are systematically reviewed in detail, especially those methods developed in the past ten years. The differences among kinds of methods, the development of each type of methods, and their applications for different flight conditions are discussed in detail. First, steady-state and several representative models are presented. The applicability of this simple model decreases when it is applied to predict the loads on small insects. Next, this paper provides a detailed description of quasi-steady (QS) models and divides these models into three groups: Osborne, Walker, and Dickinson models. Osborne models are suitable for cases with a low flight speed and flapping amplitude. Walker and Dickinson models rely on experimental and numerical data to improve the QS models for predicting nonlinear aerodynamic forces. The total forces in Walker models are divided into circulatory and non-circulatory parts. Dickinson models are established according to different high-lift mechanisms. A representative Dickinson model consists of translational, rotational, added-mass, and wake-capture components. These models provide reasonable predictions, except that their accuracy depends on empirical constants. Finally, unsteady models based on the traditional theory are examined, and several representative models are addressed. The assumption of Kutta–Joukowski conditions may not be suitable for high stroke amplitudes and flapping frequencies. Further challenges to improve aerodynamic modeling methods are mainly due to the present limited understanding of the flow complexities of various insects at low Reynold numbers.

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Recently, numerous studies have been conducted to clarify the effects of corrugation wing on aerodynamic performances. The effects of the corrugation patterns and inclination angles were investigated using computational fluid dynamic method in gliding and hovering flight at Reynolds numbers of order 104. The instantaneous aerodynamic forces and the vorticity field around the wing models were provided to research the underlying mechanisms of aerodynamic effects of corrugated wing models. The findings can be concluded as follows: (1) the corrugation patterns have different effects on aerodynamic performance. The effect of noncamber corrugated wing is to decrease the lift and increase drag compared with a flat-plate when the angle of attack is less than 25° during gliding flight. The corrugated wing with a camber (corrug-2) after the valleys enhances the aerodynamic forces when angle of attack is higher than 35°. The valley inclination angle has limited effect on aerodynamic forces in gliding flight. (2) The lift forces of different corrugation patterns show significantly asymmetric during the upstroke and downstroke. The main reason leads to this phenomenon is the case that two sides of the corrugated wings are not symmetric around the pitching axis. The corrugated wing with only two valleys (corrug-1) changes the lift and drag very slightly. Corrug-2 produces larger peak during downstroke and smaller peak during upstroke. The increase in the inclination angle has limited effect on the aerodynamic forces. The possible reason for these small aerodynamic effects might be that the corrugated wings are smoothed by small vortices trapped in valleys. The main reason for the significant difference between plate and corrug-2 is that the recirculating vortices trapped in the saddle and hump reduce the pressure above the wing surface.

Recently, numerous studies have been conducted to clarify the effects of the increases in pitching and plunging amplitudes of flapping wings on thrust and lift generation. In the present study, the effects of continuously increasing pitching and plunging amplitudes on the aerodynamic performances of a two-dimensional (2D) flapping wing are investigated computationally. Continuously increasing pitching and plunging amplitudes have significant effects on the rate of leading-edge vortex (LEV) development and the time of LEV separation; as a result, the aerodynamic performance is influenced. Lift and thrust are gradually improved with increasing pitching and plunging amplitudes; however, higher amplitudes induce the production of drag forces. Furthermore, to compare the contributions of the pitching and plunging amplitudes, we conducted simulations with pure pitching or plunging amplitude increases while keeping the other factors constant. With the increase in pitching amplitude, the vortex on the upper surface becomes weaker during the downstroke and leads to the production of a vortex on the lower surface. During the upstroke, the effect of the increase in pitching amplitude on the vortex has a symmetric influence against the downstroke. The change in pitching amplitude has little effect on the lift and thrust but leads to the production of drag forces. When the plunging amplitude increases, the LEV and the second kind of vortex, the trailing-edge vortex (TEV), becomes stronger, which will cause a concurrent increase in lift and thrust. The increase in plunging amplitude greatly improves lift and can also enhance thrust.

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