Unsteady lift for the Wagner problem in the presence of additional leading/trailing edge vortices

Abstract

This study amends the inviscid Wagner lift model for starting flow at relatively large angles of attack to account for the influence of additional leading edge and trailing edge vortices. Two methods are provided for starting flow of a flat plate. The first method is a modified Wagner function, which assumes a planar trajectory of the trailing edge vortex sheet accounting for a temporal offset from the original Wagner function given release of leading edge vortices and a concentrated starting point vortex at the initiation of motion. The second method idealizes the trailing edge sheet as a series of discrete vortices released sequentially. The models presented are shown to be in good agreement with high-fidelity simulations. Through the present theory, a vortex force line map is generated, which clearly indicates lift enhancing and reducing directions and, when coupled with streamlines, allows one to qualitatively interpret the effect of the sign and position of vortices on the lift and to identify the origins of lift oscillations and peaks. It is concluded that leading edge vortices close to the leading edge elevate the Wagner lift curve while a strong leading edge vortex convected to the trailing edge is detrimental to lift production by inducing a strong trailing edge vortex moving in the lift reducing direction. The vortex force line map can be employed to understand the effect of the different vortices in other situations and may be used to improve vortex control to enhance or reduce the lift.

Aerodynamic Analysis of a Flapping Wing Aircraft for Short Landing

“…It can be speculated that those higher-order modes are from the test rig, which has little influence on the motion of the flapping wing and aerodynamic force. According to Equations (16) and (17), the difference between the measured force with and without the wing skin results in the aerodynamic lift as shown in Figure 12a. The corresponding drag force (negative value indicates thrust) can be also obtained and shown in Figure 12b.…”

“…Wu et al [6][7][8] employed the CFD method to simulate the unsteady aerodynamics of an insect-like flapping wing and found that increased aerodynamic lift can be obtained at large flapping amplitude and large pitching angle (angle of attack, AOA) beyond the stall AoA. Based on potential flow theory [9,10] and Joukowski transformation [11,12], Ansari et al [13] constructed an unsteady aerodynamic model (UAM) to calculate the aerodynamic force produced by the leading edge vortex [14][15][16] and trailing edge vortex [17][18][19]. Chen et al [20] further developed the UAM to prevent the adverse effect of vortex penetration using a collision avoidance algorithm and enforced a zero-through-flow boundary condition for both two-dimensional (2D) and three-dimensional (3D) wings.…”

Vortex moment map for unsteady incompressible viscous flows

“…A detailed knowledge of the entire vorticity field is always required (Batchelor 1967). There has been more success with analytical-numerical coupling methods adopting unsteady thin airfoil theory corrected by additional vortices (Ramesh et al 2014;Li & Wu 2015& 2016Fernandez-Feria & Alaminos-Quesada 2018) or unsteady Blasius equation (Xia & Mohseni 2017). Advances in experimental techniques have led to accurate measurements on fluid dynamic loads on lifting surfaces (Mancini et.al 2015;DeVoria et al 2014;Ramesh et al 2014).…”

Unsteady Aerodynamics and Trailing-edge Vortex Sheet of An Airfoil

“…Another approach of modeling the wake is to fully represent the vortex sheets in the wake using discretized point vortices or vortex panels as demonstrated by Katz, 8 Jones, 9 Yu et al, 10 Pullin & Wang, 11 Ansari et al, 12,13 Shukla & Eldredge, 14 Xia & Mohseni, 15 Ramesh et al, 16 and Li & Wu. 17 Due to the high resolution of the vortical structures in the wake, the vortex-sheet methods naturally have promising accuracy, whereas the computational cost would grow as time proceeds. Recently, Xia & Mohseni 18,19 proposed a vortex-amalgamation method which effectively reduces the computational cost for large simulations.…”