Features of minimizing the induced drag of lifting systems with winglet

Аuthors

Borisova V. ^*, Silantiev V.

Siberian Aeronautical Research Institute named after S.A. Chaplygin, 21, Polzunov St., Novosibirsk, 630051, Russia

*e-mail: sa01borisova@gmail.com

Abstract

The presented article considers specifics of the aircraft lifting systems with winglets optimizing with a restriction on the geometry deformation of the base wing. The presented numerical approach to aerodynamic design allows increasing the aircraft aerodynamic lift-to-drag ratio by reducing the lifting system drag in the cruising flight mode. The drag minimization problem is focused in this article on the induced drag reducing, which is stipulated by the shroud of free vortices. The well-known Munk's stagger theorem application allows correctly compute optimal distribution of the circulation intensity in the Treftz plane and, as a consequence, find the minimum induced drag. The numerical approach to optimization is based on the idea of the aircraft lifting system replacing with a system of the discrete U-shaped vortices. According to the Munk's theorem, lifting vortex systems can be translocateed along the free-stream velocity into one vertical plane with the the air load retaining (velocity circulation) along the wingspan, which ensures an optimal solution along the lifting system. However, in the case of employing this approach for a long-range aircraft, with mainly swept wings and high subsonic cruising speeds, there is an intensive increase in the air load in the end wing sections, which increases even more, when induced drag is minimized over the entire lifting system (full optimization). This leads to the earlier compressibility stall development or the aerodynamic shock stall. In such cases, optimization of only a part of the lifting system (partial optimization) is possible, where the basic wing geometry is fixed, and the induced drag minimization is being performed on account of special wingtips or the winglets installing. In the case of the partial optimization, a fundamentally new approach, formulated in the form of a new numerical method, which accounts for the mutual interference of the wing and the winglet, both separately and on each other is employed. At the initial stage, the known initial geometry of the base wing is used and the initial geometry of the winglet is specified. Then, using a direct computational program (AEROJET program, based on the Morino’s panel method), the initial air load distribution along the wingspan and the winglet span is being determined for a given lift coefficient. This condition of retaining the air load distribution nature along the base wing span serves in a first approximation as a condition for the invariance of its geometry. The load distribution along the winglet span (wingtip) is being optimized and its geometry is being determined based on the obtained data by the proposed numerical method using the direct computational program (AEROJET). Since in view of the changes in the winglet geometry, the air load distribution along the base wing does not correspond to its geometry, the iterations continue until convergence is reached. With the new numerical approach application, optimization and aerodynamic design of the model of the advanced technology demonstrator aircraft, developed at the Siberian Aeronautical Research Institute named after S.A. Chaplygin, were performed. The aerodynamic lift-to-drag ratio increase was obtained due to the optimized winglets installation and was about 8.8%. To assess the of viscosity effect on the wake vortex computing, comparison of the results obtained by the AEROJET program (non-viscous fluid) with the results of computations by the OPENFORM program, based on the averaged Navier-Stokes equations (viscous fluid) were performed. The study of the wing model in the framework of the viscous fluid was performed with two turbulence models namely Spalart Allmaras and k–ω SST. The ordered computational grid with the corresponding block structure has a total number of elements - 10 million cells, the number of cells on the profile is 342 pieces. When analyzing the results, a good agreement between the computations for both turbulence models and with the results obtained by the new numerical approach with the correct adjustment for flow viscosity when making estimates is marked.

Keywords:

optimization, induced drag, wingtip devices, discrete U-shaped vortex, Treftz plane, circulation, aerodynamic design, turbulence model, averaged Navier-Stokes equations

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