Time Dependent Adjoint-based Optimization for Coupled Aeroelastic Problems

A formulation for sensitivity analysis of fully coupled time-dependent aeroelastic problems is given in this paper. Both forward sensitivity and adjoint sensitivity formulations are derived that correspond to analogues of the non-linear aeroelastic analysis problem. Both sensitivity analysis formulations make use of the same iterative disciplinary solution techniques used for analysis, and make use of an analogous coupling strategy. The information passed between fluid and structural solvers is dimensionally equivalent in all cases, enabling the use of the same data structures for analysis, forward and adjoint problems. Sensitivities from both forward and adjoint formulations for the fully coupled aeroelastic problem are verified using the complex step method and agreement to machine precision is demonstrated. The fully coupled adjoint formulation is then used to perform rotor blade design optimization on a Hart2 rotor in hover while constraining the time-integrated thrust coefficient to the baseline value. The optimized rotor achieves 2% reduced torque with a penalty of 1% reduction of thrust.

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