This work presents results from the application of an aerodynamic shape optimization code, Jetstream, to a suite of benchmark cases defined by the Aerodynamic Design Optimization Discussion Group. Geometry parameterization and mesh movement are integrated by fitting the multi-block structured grids with B-spline volumes and performing mesh movement based on a linear elastic model applied to the control points. Geometry control is achieved through two different approaches. Either the B-spline surface control points are taken as the design variables for optimization, or alternatively, the surface control points are embedded within free-form deformation (FFD) B-spline volumes, and the FFD control points are taken as the design variables. Spatial discretization of the Euler or Reynolds-averaged Navier-Stokes equations is performed using summation-by-parts operators with simultaneous approximation terms at boundaries and block interfaces. The governing equations are solved iteratively using a parallel Newton-Krylov-Schur algorithm. The discrete-adjoint method is used to calculate the gradients supplied to a sequential quadratic programming optimization algorithm. The first optimization problem studied is the drag minimization of a modified NACA 0012 airfoil at zero angle of attack in inviscid, transonic flow, with a minimum thickness constraint set to the initial thickness. The shock is weakened and moved downstream, reducing drag by 91%. The second problem is the liftconstrained drag minimization of the RAE 2822 airfoil in viscous, transonic flow. The shock is eliminated and drag is reduced by 48%. Both two-dimensional cases exhibit optimization convergence difficulties due to the presence of nonunique flow solutions. The third problem is the twist optimization for minimum induced drag at fixed lift of a rectangular wing in subsonic, inviscid flow. A span efficiency factor very close to unity and a near elliptical lift distribution are achieved. The final problem includes single-point and multi-point liftconstrained drag minimizations of the Common Research Model wing in transonic, viscous flow. Significant shape changes and performance improvements are achieved in all cases. Finally, two additional optimization problems are presented that demonstrate the capabilities of Jetstream and could be suitable additions to the Discussion Group problem suite. The first is a wing-fuselage-tail optimization with a prescribed spanwise load distribution on the wing. The second is an optimization of a box-wing geometry.

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.

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