Efficient Design Optimization of Vortex Generators in Subsonic Offset Inlet by Discrete Adjoint Approach

Abstract

This paper deals with the adjoint-based design optimization of vortex generators for the performance improvement of the subsonic inlet. The RAE M2129, an S-shaped inlet, was selected as the target geometry. Because of the differences in radius of curvature between the port side (outer wall) and starboard side (inner wall), a centrifugal pressure gradient that induces circulatory flow and secondary flow was developed. To minimize these detrimental aerodynamic phenomena, a design optimization of vortex generators installed in subsonic inlet was conducted. To maximize the flow quality enhancement, the effectiveness and position of vortex generator are independently optimized by using the design parameters of height, chord length, angle of incidence, axial position, and the circumferential position of each vortex generator. To increase the design efficiency, the source term model of vortex generator was employed instead of the gridded vortex generator. Since the original source term model cannot reflect a small change in position and has difficulties in differentiation for adjoint method, a differentiable source term model was developed. To deal with a large number of design variables, the gradient-based design optimization method using the discrete adjoint approach was employed to minimize the distortion coefficient while maintaining the baseline total pressure recovery ratio. As a validation of the proposed design approach, optimization with three kinds of design parameters representing the effectiveness of each vortex generator (a total of 33 design variables) was carried out with the original source term model. The designed vortex generator configuration yields a substantial improvement in inlet performance, which confirms the validity of the proposed design approach. After the validation process, a complete design with five design parameters per each vortex generator (a total of 55 design variables) was performed by using the differentiable source term model. Through the complete design process, the performance of target inlet was remarkably improved; the distortion coefficient was decreased over 79% while maintaining the total pressure recovery ratio.