Abstract
In this paper, the multi-objective, multifidelity optimization of a wing fence on an unmanned aerial vehicle (UAV) near stall is presented. The UAV under consideration is characterized by a blended wing body (BWB), which increases its efficiency, and a tailless design, which leads to a swept wing to ensure longitudinal static stability. The consequence is a possible appearance of a nose-up moment, loss of lift initiating at the tips, and reduced controllability during landing, commonly referred to as tip stall. A possible solution to counter this phenomenon is wing fences: planes placed on top of the wing aligned with the flow and developed from the idea of stopping the transverse component of the boundary layer flow. These are optimized to obtain the design that would fence off the appearance of a pitch-up moment at high angles of attack, without a significant loss of lift and controllability. This brings forth a constrained multi-objective optimization problem. The evaluations are performed through unsteady Reynolds-Averaged Navier–Stokes (URANS) simulations. However, since controllability cannot be directly assessed through computational fluid dynamics (CFD), surrogate-derived gradients are used. An efficient global optimization framework is developed employing surrogate modeling, namely regressive co-Kriging, updated using a multi-objective formulation of the expected improvement. The result is a wing fence design that extends the flight envelope of the aircraft, obtained with a feasible computational budget.
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Notes
The longitudinal moment is addressed as the pitching moment and defined as the total moment around the tranverse/lateral axis, perpendicular to the symmetry plane with its origin in the center of gravity. For equilibrium flight, this moment must equal zero. In this regard, the pitching moment coefficient of the UAV differs from the conventional pitching moment of an airfoil, which is defined around its aerodynamic center.
We assume at this point that the variations in Re during the optimization are small enough to be negligible
The constrained expected improvement is divided by the Euclidean distance of the two points farthest from each other in de objective space.
The Pareto front is the front defined in the objective space by the Pareto optimal points for which one cannot improve on one without deteriorating on the others.
The hypervolume is the Lebesgue measure contained by the attainment surface and a chosen reference points. The attainment surface was defined by Fonseca and Fleming (1996) as “the boundary in the objective space separating those points which are dominated by or equal to at least one of the data points, from those which no data points dominates or equals” and thus corresponds to the Pareto front.
The Pareto fronts are rescaled to a 1-on-1 box. This is done such that the influence of both objectives on the hypervolume is nearly equally significant.
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Acknowledgments
The authors would like to thank Prof. Dr. Ir Jan Vierendeels; his input, supervision, guidance, and support during this research has been of critical value.
Funding
This study is conducted as part of the SBO research project 140068 EUFORIA (Efficient Uncertainty quantification For Optimization in Robust design of Industrial Applications) under the financial support of the IWT, the Flemish agency of Innovation through Science and Technology. This work was carried out using the STEVIN Supercomputer Infrastructure at Ghent University, funded by Ghent University, the Flemish Supercomputer Center (VSC), the Hercules Foundation and the Flemish Government—Department EWI.
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Wauters, J., Couckuyt, I., Knudde, N. et al. Multi-objective optimization of a wing fence on an unmanned aerial vehicle using surrogate-derived gradients. Struct Multidisc Optim 61, 353–364 (2020). https://doi.org/10.1007/s00158-019-02364-x
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DOI: https://doi.org/10.1007/s00158-019-02364-x