Application of Jetstream to a Suite of Aerodynamic Shape Optimization Problems

Abstract

This work demonstrates the performance of Jetstream, a high-fidelity aerodynamic shape optimization methodology for three-dimensional turbulent flows. The geometry parameterization and mesh movement is accomplished using B-spline volumes and linear elasticity mesh movement. The Euler or Reynolds-averaged Navier-Stokes (RANS) equations are solved at each iteration using a parallel Newton-Krylov-Schur method. The equations are discretized in space using summation-by-parts operators with simultaneous approximation terms to enforce boundary and block interface conditions. The gradients are evaluated using the discrete-adjoint method to allow for gradient-based optimization using a sequential quadratic programming algorithm. The goal of this work is to investigate the performance of Jetstream for three test problems. The first problem is the drag minimization of a two-dimensional symmetric airfoil in transonic inviscid flow, under a geometric constraint that the airfoil have a thickness greater than or equal to that of a NACA 0012 airfoil. Although the shock waves are not quite eliminated, they are substantially weakened, such that the drag coefficient is reduced by 86% compared to the NACA 0012 airfoil. The second problem is drag minimization through optimizing the twist distribution of a three-dimensional wing characterized by NACA 0012 sections in subsonic inviscid flow, subject to a lift constraint. A nearly elliptical spanwise lift distribution is achieved by the optimized twist distribution, leading to a span efficiency factor of 0.98. The third problem is drag minimization through optimizing the sections and twist distribution of the blunt-trailing-edge Common Research Model wing in transonic turbulent flow, subject to lift and pitching moment constraints. For this case the optimization is performed based on the solution of the RANS equations, with the Spalart-Allmaras turbulence model fully coupled and linearized. The drag coefficient is reduced by eleven counts, or 6%, when analyzed on a fairly fine mesh.