Adjoint-Based Design Optimization of Vortex Generator for Three-Dimensional Internal and External Viscous Flows

Abstract

validating the proposed design approach, obtaining the optimized vortex generators, and confirming their enhanced performance. Through the proposed design process, the performance of the target inlet was remarkably improved, showing that the distortion coefficient decreases well over 70% while maintaining the total pressure recovery ratio. For the DLR-F6 wing-body aircraft, the parametric study and the design study relating to the vortex generator were performed to increase the ratio of lift to drag by removing the junction vortex. To check the flow characteristics of the wing-body junction and to confirm the effects of the vortex generator on the junction vortex, a total of nine parametric studies were conducted first, and a baseline configuration of design was determined based on this results. As a result of the parametric study, the lift to drag ratio of DLR-F6 increases by over 2~4% under the same flight conditions. After carrying out the optimization of the vortex generators, the junction vortex was shrunk and weakened, and the performance of the DLR-F6 improved over 5% without any additional components what can be a cause of weight increase except the vortex generators.

This study focused on an adjoint-based design optimization of vortex generators for the performance improvement of an aircraft. Among the several components of the aircraft, the applications of this study included the internal flow of an S-shaped subsonic inlet (S-duct), the RAE M2129, and the external flow of a wing-body configuration, the DLR-F6. To improve these components and to validate the proposed design approach on both of internal and external flows, the vortex generators were installed inside the S-duct and on the wing upper surface. Then they were independently optimized with five design parameters per each vortex generator. For the purpose of truly optimal design, each vortex generator should be independently treated by fully reflecting local flow patterns near the vortex generators. To increase the efficiency of flow analysis and design, the source term model of the vortex generator, the BAY model, was employed. The original BAY model did not reflect a small change in position, so it had difficulties in differentiation for sensitivity analysis of the vortex generator. The BAY model, therefore, was modified into a differentiable BAY model by taking into account a small volume change. For the optimal design mentioned above, each vortex generators must be dealt with independently

thus, a large number of design variables were considered. Because the gradient-based design optimization using the discrete adjoint approach has an advantage in that the number of design variables is independent of the computational cost, a sensitivity analysis with respect to the design variables was performed by using the adjoint variable method including the original/differentiable BAY model. For the RAE M2129, the design of vortex generators was performed to minimize the distortion coefficient while maintaining the baseline total pressure recovery ratio by adopting the proposed gradient-based design process that included the source term model. A total of five design cases were conducted to achieve 3 objectives