Accurate induced drag prediction for highly non-planar lifting systems

For highly non-planar lifting systems like the box wing, induced drag predictions based on common potential-flow methods can have limited accuracy. This is primarily related to the linear, fixed-wake surrogate models, which neglect the correlation of the effective height-to-span ratio and system angle of attack or insufficiently account for free-wake deformations such as deflection and roll-up effects.

Dependent on the vertical and horizontal wing arrangement of simplified box wing and biplane configurations and the system angle of attack, the present research analyses the unknown impact of wake model effects, investigates the accuracy of potential-flow induced drag predictions against an Euler-flow reference and explores the influence of higher-order wake effects. The computational expense of considered methodologies is assessed to evaluate their applicability within an aerodynamic design and optimization methodology for highly non-planar lifting systems.

Under certain conditions, higher-order wake and wake surrogate effects are confirmed to impact on the induced drag prediction. The body-fixed wake model is found generally inappropriate for induced drag estimation of present lifting systems, whereas the freestream-fixed wake model provides consistent results. Positive-staggered systems at positive angels of attack are found particularly prone to higher-order wake effects, due to the vertical contraction of wake trajectories, which leads to smaller effective height-to-span ratios than compared with negative stagger and thus closer interactions between trailing wakes and lifting surfaces. A relaxed, force-free wake model is found compulsory to enable fast but accurate induced drag predictions when using potential-flow methods for the analysis of highly non-planar lifting systems with significant positive stagger.