Aerodynamic Shape Optimization of Benchmark Problems Using Jetstream

Abstract

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.

Multilevel Subdivision Parameterization Scheme for Aerodynamic Shape Optimization

“…This resulted in a significant reduction in overall computation time. It was also found to increase the chances of a similar solution being found when multiple solutions exist 59,60 . This is believed to be the main contributor to the improvement in results compared to previous work from the authors 58,61 .…”

“…A considerable number of papers have been published on this case 1,2,52-60 and it has been shown to be a particularly difficult problem due to a range of characteristics such as multiple local minima 58 , non-symmetric solutions 59 and hysteresis 60 . In this previous work, results ranging from 100 to 25 drag counts have been reported with the best cases produced by Lee Due to the symmetry of the problem a symmetry plane was aligned with the aerofoil chord and just half the mesh was solved.…”

Progressive Subdivision Curves for Aerodynamic Shape Optimisation

“…This is the inviscid drag reduction of a NACA0012 at M = 0.85 and α = 0. A considerable number of papers have been published on this case [1,2,46,47,48,49,50,51,52,53,54] and it has been shown to be a particularly difficult problem to optimise due to a range of characteristics such as multiple local minima [52], non-symmetric solutions [53] and hysteresis [54].…”

Global Optimization of Multimodal Aerodynamic Optimization Benchmark Case

“…As such, the AIAA Aerodynamic Design Optimization Discussion Group (ADODG) a was formed. As part of this, a number of inviscid and viscous aerofoil and wing optimization cases were suggested, with a number of research groups presenting results; see [13][14][15][16][17][18][19][20] for example.…”