Applications of a discrete viscous adjoint method for aerodynamic shape optimisation of 3D configurations

Abstract

Within the next few years, numerical shape optimisation based on high-fidelity methods is likely to play a strategic role in future aircraft design. In this context, suitable tools have to be developed for solving aerodynamic shape optimisation problems, and the adjoint approach-which allows fast and accurate evaluations of the gradients with respect to the design parameters-is proved to be very efficient to eliminate the shock on aircraft wing in transonic flow. However, few applications were presented so far considering other design problems involving 3D viscous flows. This paper describes how the adjoint approach can also help the designer to efficiently reduce the flow separation onset at wing-fuselage intersection and to optimise the slat and flap positions of a 3D high-lift configuration. On all these cases, the optimisations were successfully performed within a limited number of flow evaluations, emphasising the benefit of the adjoint approach in aircraft shape design.

Drag Minimization Based on the Navier–Stokes Equations Using a Newton–Krylov Approach

“…The gradient of the Lagrangian function must also be sufficiently small, satisfying (22) where g represents the gradient, and are the adjoint variables within SNOPT's internal Lagrangian merit function. The tolerance e for the gradient is typically 1 x 10-5; however, this level o f convergence is often not achieved.…”

“…Nielsen and Anderson [20] presented examples of discreteadjoint-based optimization based on the three-dimensional RANS equations and the Spalart-Allmaras turbulence model and showed the negative impact that certain simplifications of the linearization have on the gradient accuracy, including freezing the turbulence model. Brezillon et al [21 ] demonstrated improved performance of the DLR-F6 wing-body configuration with an approach based on the unstructured parallel RANS solver, TAU, and discrete-adjoint gradients; this work was extended to show how the optimization algorithm can be used to reduce the area of flow recirculation at a w ingbody junction and to optimize the slat and flap positions for a threedimensional high-lift configuration [22], A good summary of the state of the art of RANS-based aerodynamic shape optimization is provided by Epstein et al [23], who applied three state-of-the-art optimization methodologies to the same constrained design problem and demonstrated similar improvements in drag at the main design point and good performance at off-design conditions. Note, however, that the shape changes in the design problem used in their study are quite small, and no indication is given as to how the methodologies would perform in an optimization with larger shape changes.…”

Aerodynamic Shape Optimization of a Box-Wing Regional Aircraft Based on the Reynolds-Averaged Navier-Stokes Equations

“…Meanwhile, Brezillon et al [51] developed an unstructured flow solver and used it with the discrete-adjoint method to study high-lift wing configurations [52] and wing-body junctions [53].…”

Strategies for Solving High-Fidelity Aerodynamic Shape Optimization Problems

“…With an efficient adjoint implementation, the cost of computing the gradient of a single function of interest with respect to hundreds or thousands of shape design variables is roughly of the same order of the cost of one flow solution [6]. Those methods have been successfully applied in recent aerodynamic shape optimizations [7,8,9,10,11,12].…”