Effect of Small-Scale Output Unsteadiness on Adjoint-Based Sensitivity

This paper investigates the impact of small-scale unsteadiness on adjoint-based output sensitivity analysis. In particular, when iterative methods for nonlinear flows fail to converge to a steady state, it is demonstrated that the resulting sensitivity analysis can be highly inaccurate, evenwhen the unsteadiness in the outputs is small. The specific example considered is the viscous subsonic flow around an airfoil over a range of angles of attack. If a strengthened solver is used to solve the adjoint equation (even though the flow equations did not fully converge), it is demonstrated that the sensitivity of the lift with respect to angle of attack can vary significantly, due to linearizing about different solution iterates of the steady flow solver. Further, the unsteady iterates from the time-inaccurate steady-state solver to the time-accurate solution are compared. The unsteadiness of the time-accurate solution is markedly different from the iterate solutions of the steady-state solver. If a strengthened solver is applied to the nonlinearflow equations, steady solutions can be achieved whose lift is significantly different from the time-averaged lift of the time-accurate simulations. Time-accurate unsteady adjoint analysis is then shown to provide accurate sensitivities for the timeaveraged lift.