Dynamic similar models are designed to study the flight behavior of the full-scale aircraft in early design stages. Due to physical and operational constraints, full dynamic similarity between the scaled-down model and full-scale aircraft is not feasible. Thus, the scale model would be flying at different Reynolds number and Mach number. A given aircraft configuration with specific aerodynamic characteristics will have different performance if Mach number and Reynolds number are changed considerably, which results in different dynamic behavior of the scale model. To compensate for these dissimilarities, it is proposed to modify the airfoil geometry of the scale model to preserve aerodynamic similarity. In this study, based on the flight regime and design requirements, maximum thickness of the airfoil, maximum camber, and their respective location are modified to preserve aerodynamic characteristics at different Mach and Reynolds numbers. Geometry optimization was performed using Particle Swarm Optimization and the geometry optimization results show that it is possible to mitigate the change in Reynolds and Mach number in various flight conditions. It has been shown that optimized geometries of all test cases had airfoils with lower maximum thickness and slightly higher maximum camber.
In this paper, a new approach for multi-objective robust optimization of flutter velocity and maximum displacement of the wing tip are investigated. The wing is under the influence of bending-torsion coupling and its design variables have different levels of uncertainty. In designing and optimizing wings with a high aspect ratio, the optimization process can be done in such a way to increase the flutter velocity, but this can increase the amplitude of the wing tip displacement to a point that leads to the wings damage and structural failure. Therefore, single-objective design optimization may lead to infeasible designs. Thus, for multi-objective optimization, modeling is based on the Euler-Bernoulli cantilever beam model in quasisteady aerodynamic condition. Using the Galerkin's techniques, the aeroelastic equations are converted to ODE equations. After validating the results, the system time response is obtained by the numerical solution of the governing equations using 4th Runge-Kutta method and the flutter velocity of the wing is obtained using the theory of eigenvalues. Subsequently, by choosing bending and torsional rigidity and mass per unit wing length as the optimization variables, using Monte Carlo-Latin hypercube (MC-LH) simulation and 4th polynomial chaos expansion (PCE), the effect of uncertainty on these variables is modeled in modeFRONTIER™ software coupled with MATLAB™ and optimization is performed by genetic algorithm. Finally, by plotting the Pareto front, it is observed that with an acceptable increase in flutter velocity, the maximum wing displacement amplitude is reduced as much as possible. The results of the multi-objective robust optimization show more feasible results compared with deterministic optimization.
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