Conceptual Design of Swept-Wing Root Airfoils

Abstract

For modern transonic transport aeroplanes, it is important to produce low drag at high cruise speeds. The root effect, caused by effects of symmetry on swept wings, decreases the performance of these aeroplanes. During aeroplane design, root modifications are applied to counteract this decrease in performance. Most conceptual aeroplane design tools do not have a method for design of the root aerofoil. However, the design of the root aerofoil has a significant influence on the properties of the final design, since it transfers the loads from the wing to the fuselage. Therefore, having a conceptual method for design of the wing root aerofoil will increase the accuracy of a conceptual aeroplane design. For conceptual design, computational times are important, to allow the designer to try different approaches and get a feel for the design. In this report a method is developed to approximate the root aerofoil design to achieve straight isobars on a wing of any given shape, within computational times that are suitable for conceptual design. First a method is developed for estimating the pressure distribution over the root aerofoil of a given wing. This is done by combining a method for estimation of the root effect due to thickness, a method for estimation of the root effect due to lift, a Vortex Lattice Method (VLM) and a two-dimensional panel method. A full potential method, MATRICS-V, is used to verify the results of the method, because of its proven validity. It is shown that the results of the first part of the method are generally in good agreement with results found by MATRICS-V. The effects of wing sweep, wing taper and addition of a wing kink can be modelled with results that are in good agreement with the verification data. For aft swept wings with positive lift, the pressure near the leading edge is underestimated. For forward swept wings with positive lift, the pressure on the upper surface is overestimated. For wings with a cambered aerofoil an inaccuracy occurs over the forward part of the profile. The general shape of the curve, however, is captured. Secondly, this method is coupled with an optimisation method for the root aerofoil, using Class-Shape function Transformation (CST) parametrisation. The target of the optimisation is set to achieve a similar pressure distribution over the wing root aerofoil as the pressure distribution over the outboard section of the wing. For the developed method, it is difficult to show that the results are valid, since there is no method that has a one-to-one match with the method developed. Therefore, the results are compared to the general characteristics observed in actual root aerofoil designs. The method shows the characteristic behaviour in terms of change in camber, change in location of maximumthickness and change in incidence angle. The increase in thickness, however, is not present. This is caused by the fact that the lower surface pressure distribution is also set as a target. In actual aeroplane design the lower surface is of less importance. In the method developed, however, it is of importance to retain the shape of specific aerofoil designs, like supercritical aerofoils, during optimisation. As a final verification, an optimised root aerofoil design is analysed using MATRICS-V. The results show that the root section pressure distribution is in good agreement with the outboard pressure distribution. In terms of computational time, the method is shown to generally produce reliable results within 30 seconds.