Adjoint State of Nonlinear Vortex-Lattice Method for Aerodynamic Design and Control

Abstract

The adjoint state of a nonlinear vortex-lattice method, coupled with sectional polars obtained with an infinite swept-wing (2.5D) Reynolds-averaged Navier–Stokes (RANS) solver, is presented as an interactive method for preliminary aerodynamic design and control of moderate-to-high aspect ratio wings in subsonic and transonic flows. First, the nonlinear vortex-lattice method is described, augmented with a Prandtl–Glauert compressibility correction and regularized so that poststall solutions can be recovered. The linearization of the coupled system of equations is formulated using a Newton method, and the adjoint state is obtained for lift, drag, and inverse design functionals. Numerical results show that the aerodynamic model approximates well the forces predicted by three-dimensional (3D) RANS simulations for the Common Research Model wing, and that the adjoint-state gradients agree well with finite difference tests for a plethora of test cases. More interesting examples are shown, ranging from the optimal unstalling of wings to the assimilation of 3D RANS data into the present model, as well as its ability to extrapolate.