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A Time-Spectral Adjoint Approach for Aerodynamic Shape Optimization Under Periodic Wakes

TitleA Time-Spectral Adjoint Approach for Aerodynamic Shape Optimization Under Periodic Wakes
Publication TypeConference Papers
Year of Publication2020
AuthorsHe, P, Luder, AJ, Mader, CA, Maki, KJ, Martins, JRRA
Conference NameAIAA Scitech 2020 Forum

Design problems in aerospace engineering often involve periodic unsteady flow, and understanding its characteristics provides useful insights for the design. Aerodynamic shape optimization has been widely used to reduce the design period for steady-flow problems; however, its application for unsteady flow remains challenging due to its high computational cost and memory usage. In this paper, an approach is proposed to reduce the cost of aerodynamic shape optimization for unsteady flow problems. The proposed approach uses the time-spectral method to simulate flow and compute derivatives. Specifically, it uses a fully-segregated, block Gauss--Seidel (FSBGS) method to solve the time-spectral flow equations. The FSBGS formulation requires minimal memory overhead and code modification effort, compared with a fully-coupled time-spectral formulation. A discrete adjoint approach is then used to compute derivatives for the time-spectral flow solver. The diagonal blocks in the time-spectral Jacobian are assembled by reusing the steady-state Jacobians from each time instance, while the off-diagonal blocks are computed analytically. The NACA0012 airfoil is selected as the baseline geometry, and an oscillating source term is added in the momentum equation to mimic periodic wakes. The time-spectral flow solver is verified by comparing the simulated time-series of drag and lift with those simulated by the time-accurate method. The performance of the time-spectral flow and adjoint solvers are evaluated in terms of speed, memory usage, and accuracy. Finally, the implemented solvers are incorporated into a gradient-based optimization framework to perform aerodynamic shape optimization under periodic wakes. The averaged drag reduces by 10.5\% and the lift constraint is satisfied. The proposed method has the potential to reduce the computational cost for analyzing and designing engineering systems that involve periodic wakes, e.g., propeller-wing interaction for electric aircraft and stator-rotor interaction for turbomachinery.

Citation Key1347