Thrust Generation of Heaving Foil in Microflow

THE flight using flapping wings, inspired by small bird flight, has been studied extensively with the development of ornithopter-type micro air vehicle (MAV) [1-3]. Recently, nano air vehicle (NAV), a smaller vehicle that mimicks tiny insects, has also been introduced and under construction. The ultimate miniaturization technology of the flapping flight for military applications can be applied to minimally invasive surgeries (MIS) or drug delivery [4]. Because of the extremely small-sized wings, flow conditions around them are placed in a microflow regime, commonly defined as the Reynolds number (Re) ranging between 0.01 and 100 [5]. In the microflow regime, the experimental studies have still faced difficulties in measuring small aerodynamic forces generated by the flapping motions of tiny wings. Numerical studies of several researchers reported that, below a certain Re, lift is not generated and the leading- and/or trailing-edge vortices disappear or do not form [6-9]. In our previous study, we found that the airfoil should generate the reverse von Karman vortex streets with strong vorticity to overcome drag [10]. It is also well known from the results of [11-14] that the changes of the wake pattern behind a flapping wing are closely related to the variation of Strouhal number (St(a)) at a given Re. Therefore, St(a) is another parameter for determining the thrust generation at a given Re [15]. Several published papers have studied much of the critical Re and St(a) relationship for the aerodynamic transition from drag to thrust [16-21]. To fully explain propulsive forces of micro flapping robots, two important factors must be taken into account: three-dimensional (3-D) kinematics and morphology of wing motions. Many researchers have studied on insect flight from this point of view [8-22] with the development of numerical simulation methods and computer capacity. However, not much has been disclosed on the thrust generation behavior of flapping airfoils in microflow regime. In this note, using a numerical simulation based on a lattice Boltzmann method (LBM), the minimum St(a) (St(a,min)) that is required for thrust generation by a heave oscillating wing is proposed as a function of Re. Although this study is limited to the two-dimensional flat plate wing, the results will explain the thrust effect in terms of the aerodynamics changing significantly in microflow.