Aerodynamics of thin permeable wings

Abstract

The introduction of permeability to aerodynamic lifting surfaces changes the lift, drag, and pitching moment characteristics. While numerous approaches to calculate these effects exist, no simple estimation method is available. The present work is motivated by the permeability effects visible in wind tunnel tests of a replica of Otto Lilienthal’s 1895 Normalsegelapparat. They prompted the formulation of a simple analytical theory by Prof. Dillmann and serve as a full scale case of the effect. In the present thesis, the simple, analytical theory, which correlates the permeability and porosity properties of a lifting surface with a local change in angle of attack and the resulting lift and drag changes, is reported and extended by a quadratic formulation of the permeability. The theory is compared against a small scale experiment and the full scale results from the Normalsegelapparat. The small scale experiment consists of a low-aspect-ratio wing in an open wind tunnel. The wing, which is covered with several thin fabrics featuring permeabilities between 78.3 Pa s/m and 795.8 Pa s/m, is investigated at chord-based Reynolds numbers around 3 × 105. Both the near surface and global flow fields around the wing are recorded in a plane at 62.5 % semi-span using a planar PIV setup. In addition, the impermeable small scale configuration is modeled in two- and three-dimensional CFD calculations in order to verify the wind tunnel results. The correlation between permeability and a change in local angle of attack is confirmed. However, the choice of porosity as the proportionality constant can not be verified. The PIV flow field indicates that a low velocity region forms near the trailing edge, which deflects the stream lines around the wing and causes a decambering effect. In contrast, the analytical theory predicts a perpendicular flow through the wing superimposed on the surrounding flow, which leads to a similar decambering. The correlation found in the full scale case exhibits a different proportionality constant for the same fabric. This confirms that the proportionality constant must be dependent on external factors such as the wing planform. In addition, the flight performance and characteristics of the Normalsegelapparat and the influence of permeability are discussed in detail. The main conclusion of this thesis states that the presented analytical theory works in principle, but its proportionality constant is configuration dependent because the observed mode of action differs from the underlying assumptions.