Method for Accountting the Effect of End Washers on the Flow Around the Wing with Spanwise Profiles

Abstract

Purpose of research is to develop a method for accounting for the influence of end washers on the flow of wings with an arbitrary distribution of fillets over the span.Methods. The installation of end washers significantly improves the aerodynamics of the wing, increasing lift and reducing inductive resistance. The theory of a continuous vortex surface is applied to simulate the effect of end washers on the flow of a volumetric wing. In accordance with it, oblique horseshoe-shaped vortices that model the upper and lower sides of the wing are continuously distributed along the longitudinal panels, into which the half-span of the wing is divided. The bearing parts of each horseshoe-shaped vortex lie in planes parallel to the plane of the wing chords and pass through the points and the middle section of the panel at which the induced velocities are calculated. The free vortices of the wing descend from its ends from the upper and lower surfaces at an angle to the plane of the chords.Results. An algorithm has been developed for calculating the intensity of vortices from the non-permeability condition, taking into account the attached and free vortices of the wing and the end-washer vortices. The vortex densities included in this condition are represented by trigonometric series. The developed method takes into account the geometry of the profile and end washers, the shape of the wing in the plan. The vortices induce an additional velocity at the points on the surface of the wing. To calculate their values, the Biot-savard formula on vortex influence is used.Conclusion. A method for calculating the aerodynamic characteristics of a volumetric wing with end washers has been developed from the unified positions of the theory of a continuous vortex surface. The calculations take into account the geometry of the washers and profile, the shape of the wing in the plan. The method is universal and can be used for wings without washers, including for thin ones.