Use of Lift Superposition for Improved Computational Efficiency of Wing Post-Stall Prediction

Abstract

Recently a novel scheme, based on an iterative decambering approach, was developed at NC State University for the prediction of post-stall characteristics of wings using known section data as inputs. The scheme, suitable for implementation in lifting-line and vortexlattice methods (VLM), differs from earlier approaches in the procedure for computing the residual for the Newton iteration. This paper presents an improvement to the decambering approach in which, superposition of lift distributions is used for computing the Jacobian and residual for the Newton iteration. With this improvement, basic and additional lift distributions are first pre-computed and stored. This information is subsequently used in the post-stall computations without the need for VLM in the iterative computations. As a result, the efficiency of the computations is increased and the post-stall computations can be done without the restriction of having a VLM in the loop. I. Introduction The ability of linear aerodynamic methods such as lifting-line theory (LLT), Weissinger’s method, and vortex-lattice methods (VLM) to successfully predict the lift and induced drag behavior of medium to high aspect ratio wings is well established. In these methods, a linear lift curve with a slope of approximately 2� per radian is typically assumed for the airfoil sections that form the wings. For several decades, researchers have sought to extend the capability of these linear prediction methods to include the aerodynamic analysis of wings with nonlinear airfoil lift curves. These efforts were motivated by the desire to predict stall and post-stall aerodynamic characteristics of wings using experimental or computational aerodynamic data for the airfoil sections at post-stall conditions. It is recognized that the flow over a wing at post-stall conditions is highly three dimensional and the use of a quasi-two-dimensional approach represents a significant approximation. The impetus for such a prediction method, however, is provided by the need for rapid aerodynamic prediction capabilities for such high-alpha conditions for aircraft stability and control, simulations, and in the early phases of vehicle design. Furthermore, even high-order computational fluid dynamics (CFD) techniques are only now approaching the stage where they can be reliably used for high-alpha aerodynamic prediction. These CFD high-alpha analyses, however, require massive computing resources and significant time for analysis at even a single angle of attack. Thus the search for rapid, albeit approximate, approaches for stall and post-stall prediction of wings using known section data continues to be of interest. The traditional approaches for extending linear aerodynamic prediction methods to handle nonlinear and post-stall airfoil lift curves can be broadly classified into two kinds: the iterative -distribution approach and the �-correction approach. In the first approach, a lift distribution is first assumed on the wing. The distribution is then iteratively corrected by determining the effective-� distribution using the nonlinear airfoil lift curve. In the second approach, the deviation of the airfoil nonlinear lift curve from the potential-flow !