Recent progress in aerodynamic modeling methods for flapping flight

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.