Optimization of Flap Position Using a Modified Discrete-Vortex Method

The work proposes the use of a low-fidelity discrete-vortex-method-based model for function evaluation in genetic-algorithm-based optimization cycles toward optimizing the flap position of a high-lift configuration. The proposed methodology is a two-step strategy. In the first step, a modified discrete-vortex method is employed to obtain a vortex distribution for a given reference configuration for which the aerodynamic coefficients are known from a high-fidelity computational fluid dynamics solver. A constrained minimization procedure is employed to match the aerodynamic coefficients as computed using the modified discrete-vortex method with those obtained using the high-fidelity solver. The use of drag panels in the modified discrete-vortex method allows drag predictability even though the underlying procedure is based on a potential flow theory. In the second step, the model based on the discrete-vortex method is employed to obtain aerodynamic coefficients for any new configuration that can be considered as a perturbation around a reference configuration. The reference configuration is chosen based on a proximity criterion. The cost effectiveness of the proposed strategy allows the use of multiple optimization cycles, each with a large population size, with the high-fidelity reference data getting enriched at the end of every optimization cycle, particularly in the region of optimality. As the optimization cycles evolve, the model becomes progressively more accurate. The effectiveness of the present optimization strategy is demonstrated for the flap-position optimization of a high-lift airfoil corresponding to a takeoff configuration of a conceptual Regional Transport Aircraft