Aiaa 2003–1097 an Iterative Decambering Approach for Post-stall Prediction of Wing Characteristics Using Known Section Data

An iterative decambering approach for the post stall prediction of wings using known section data as inputs is presented. The method can currently be used for incompressible flow and can be extended to compressible subsonic flow using Mach number correction schemes. A detailed discussion of past work on this topic is presented first. Next, an overview of the decambering approach is presented and is illustrated by applying the approach to the prediction of the two-dimensional C l and Cm curves for an airfoil. The implementation of the approach for iterative decambering of wing sections is then discussed. A novel feature of the current effort is the use of a multidimensional Newton iteration for taking into consideration the coupling between the different sections of the wing. The approach lends itself to implementation in a variety of finite-wing analysis methods such as lifting-line theory, discrete-vortex Weissinger's method, and vortex lattice codes. Results are presented for a rectangular wing for α from 0 to 25 deg. The results are compared for both increasing and decreasing directions of α, and they show that a hysteresis loop can be predicted for post-stall angles of attack. Nomenclature C damping factor C L wing lift coefficient C l airfoil lift coefficient C m airfoil pitching moment coefficient about the quarter chord c chord F residual vector f element of residual vector i, j index of wing section J Jacobian matrix LLT lifting line theory N number of wing sections VLM vortex lattice method x 2 chordwise start location of the second decam-bering function α angle of attack β angle of yaw Γ strength of bound vortex δx vector containing the corrections to the New-ton variables δ 1 (x) first decambering function δ 2 (x) second decambering function θ 2 (x) angular coordinate corresponding to x 2 Subscripts max maximum sec represents value for a wing section visc represents value from two-dimensional viscous experimental or computational data