A high-order sensitivity method for multi-element high-lift device optimization

• Ability of method to optimize high-lift devices with a three-element configuration.
• Computational efficiency with mixed geometric and flow parameters.
• Sensitivity of L1T2 slat (ERCOFTAC benchmark) to the flow conditions.
• Original lens-shape grid topology for flexible angle-of-attack study.
• Importance of high-order derivatives and cross-derivatives on flow features (drag).

A complete procedure to study and optimize a multi-element high-lift device is presented and applied to the L1T2 test case. The direct Reynolds-Averaged Navier–Stokes (RANS) simulations of the reference configuration first reveal the importance of the size of the computational domain to correctly capture the potential effects generated by the L1T2 configuration. A parameterized Navier–Stokes approach based on a high-order sensitivity technique is then used as a surrogate model for solution reconstructions. This approach has the advantage to ask for only one parameterized RANS simulation around a reference configuration. The results stress the importance to account for higher derivatives and turbulence effects for such non linear parameters as the drag. They also help assess the strong coupling between certain parameters such as the flap and slat rotations. Then, the high-lift device is optimized according to two illustrative objectives: maximize the lift and minimize the drag. A genetic algorithm is applied to construct the Pareto front. Optimizations using only the geometric parameters (geometrical optimization) or the geometric parameters and the inlet flow Mach number and angle of attack (total optimization) are performed. Both optimizations show quite similar optimal geometric positions: a flap rotation inducing the maximum camber to increase the lift and an upward slat rotation to reduce the drag according to the parameter coupling study. In the total optimization, configurations with higher lift coefficients are found by setting the angle of attack and the Mach number to their maximum values. This optimization allows obtaining more important variations of the lift and the drag from the baseline configuration than the geometrical optimization.