Abstract
For staggered boxwings the predictions of induced drag that rely on common potential-flow methods can be of limited accuracy. For example, linear, freestream-fixed wake models cannot resolve effects related to wake deflection and roll-up, which can have significant affects on the induced drag projection of these systems. The present work investigates the principle impact of wake modelling on the accuracy of induced drag prediction of boxwings with stagger. The study compares induced drag predictions of a higher-order potential-flow method that uses fixed and relaxed-wake models, and of an Euler-flow method. Positive-staggered systems at positive angles of attack are found to be particularly prone to higher-order wake effects due to vertical contraction of wakes trajectories, which results in smaller effective height-to-span ratios than compared with negative stagger and thus closer interactions between trailing wakes and lifting surfaces. Therefore, when trying to predict induced drag of positive staggered boxwings, only a potential-flow method with a fully relaxed-wake model will provide the high-degree of accuracy that rivals that of an Euler method while being computationally significantly more efficient.
Highlights
Induced drag is an inviscid phenomenon and originates in the opposed spanwise flow patterns on the upper and lower wing surface that is the result of the spanwise pressure gradients of a finite wing generating lift
Against the background of the objectives set in Flightpath 2050 [2], measures that provide lower induced drag support the efforts to attain a cutback in fuel consumption and climate reactive emissions
The lift is computed along the continuous lifting lines that represent the wing, whereas the induced drag is estimated by taking the cross product between the circulation that is shed into the wake at the trailing edge and the velocity induced by the wake at this spanwise location [36,37]
Summary
Induced drag is an inviscid phenomenon and originates in the opposed spanwise flow patterns on the upper and lower wing surface that is the result of the spanwise pressure gradients of a finite wing generating lift. Because tangential velocities around the side-edge of a wingtip can become very large, a viscosity induced flow separation occurs This causes initial roll-up of the wake and shifts the tip vortex inwards [6], altering the trailing wake shed compared to an inviscid computational solution. The inviscid aerodynamic advantage of these configurations can primarily be related to the bound circulation being distributed over a larger effective wingspan This lowers the spanwise loading and reduces the average downwash velocity of the system compared to that of an optimally-loaded planar wing of equivalent span and lift [1]. Based on linear potential-flow theory, the boxwing achieves the highest span efficiency or lowest induced drag for a given projected wingspan and lift [7,13,14,15,16,17,18]
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