Unsteady Thin-Airfoil Theory Revisited: Application of a Simple Lift Formula

Abstract

The physical foundations of unsteady thin-airfoil theory are explored in the general framework of viscous flows. The thin-airfoil lift formula is derived by using the simple lift formula that contains the vortex lift and the lift associated with the fluid acceleration. From a broader perspective, the thin-airfoil lift formula could be applicable even when the flow around an airfoil is moderately separated, from which the classical von Kármán-Sears lift formula can be recovered as a reduced case. The quantitative relationship between boundary layer and lift generation is discussed. Direct numerical simulations of low-Reynolds-number flows over a flapping flat-plate airfoil are conducted to examine the accuracy and limitations of the thin-airfoil lift formula.

Explicit Role of Viscosity in Generating Lift

“…(4), the steady low-Reynolds-number flow over a two-dimensional flat plate at a small angle of attack (AOA, denoted by α) is considered as an example [12][13][14]. As shown in Fig.…”

“…Furthermore, to elucidate the relationship between boundary layer and vortex lift, the viscous flow over a flat plate can be discussed from another perspective [14]. As shown in Fig.…”

The Lift Problem in Flapping Forward Flight at Low Reynolds Numbers

“…(3), the physical foundations of the unsteady thin airfoil theory are explored in the viscous-flow framework (Liu et al 2014). A 2D attached flow field over a thin airfoil can be decomposed into the outer potential flow and the boundary layer (or the viscous flow region).…”

“…The kinematic parameters in the four cases studied in DNS are given in Table 1. The flow around the flapping airfoil is determined by the incompressible NS equations (Wang et al 2014). The Reynolds number based on the chord length of the plate and uniform upstream flow is 300 / Uc Re    .…”

“…Similarly, to compare the wings with the dynamically changing wingspan and the fixed wingspan, the increment of ) t ( Cl is given by Numerical simulations of the low-Reynolds-number flows around the flapping rectangular morphing wing are conducted in the parametric space by using the immersed boundary method (Wang et al 2014). Figure 9 shows the 3D flow structures viewed from…”