Adjoint-Based Unsteady Airfoil Design Optimization with Application to Dynamic Stall

This paper presents the development and application of an adjoint-based optimization method to designing airfoils with the objective of alleviating dynamic stall effects in helicopter rotor blades. The unsteady flow problem is simulated using the NSU2D code, which is a two-dimensional unsteady, viscous, turbulent Reynolds averaged Navier-Stokes (RANS) finite-volume solver. The corresponding adjoint code computes sensitivities of the optimization objective functions with respect to a set of design inputs and is developed through discrete linearization of all components building up the flow solver. Objective functions are defined such that their minimization results in alleviation of undesirable dynamic stall characteristics while the design inputs are parameters that control the shape of the airfoil. The method is applied to an example problem where the goal is to reduce the peak pitching moment during the hysteresis cycle of the SC1095 airfoil while maintaining the baseline time-dependent lift profile. To our knowledge, this work represents the first application of the unsteady adjoint method to optimizing airfoil geometry in dynamic stall problems.