A review on aerodynamic optimization of turbomachinery using adjoint method

Improvements in aerodynamic turbomachinery design have gained attraction due to the increased demand for a more sustainable future. Several optimization approaches have been presented and employed in the realm of aerodynamic design. However, among all of them, the adjoint approach has emerged as a hot research topic for aerodynamic optimization in the field of turbomachinery. The ability of this method to efficiently compute the derivatives of objective functions for several design variables has made it a promising optimization tool. This study provides a comprehensive review of all significant studies undertaken since the turn of the 21st century when the adjoint method was employed for the aerodynamic optimization of turbomachinery applications. The application of the adjoint approach in that context is extensively discussed under various aspects, including shape optimization in both steady and unsteady flows, varied eddy viscosity, non-ideal compressible fluid-dynamics, multi-objective and multi-point optimizations, multidisciplinary optimization, coupling adjoint method with other approaches, parametrization methods, and uncertainty quantification. Finally, the review concludes by highlighting key points and outlooks on future developments.