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

Abstract

A methodology is presented for performing numerical aerodynamic shape optimization based on the threedimensional Reynolds-averaged Navier-Stokes (RANS) equations. An initial multiblock structured mesh is first fit with B-spline volumes that form the basis for a hybrid mesh movement scheme that is tightly integrated with the geometry parameterization based on B-spline surfaces. The RANS equations and the one-equation Spalart-Allmaras turbulence model are solved in a fully coupled manner using an efficient parallel Newton-Krylov algorithm with approximate-Schur preconditioning. Gradient evaluations are performed using the discrete-adjoint approach with analytical differentiation of the discrete flow and mesh movement equations. The overall methodology remains robust even in the presence of large shape changes. Several examples of lift-constrained drag minimization are provided, including a study of the common research model wing geometry, a wing-body-tail geometry with a prescribed spanwise load distribution, and a blended-wing-body configuration. An example is provided that demonstrates that a wing optimized based on the Euler equations exhibits substantially inferior performance when subsequently analyzed based on the RANS equations relative to a wing optimized based on the RANS equations.1555

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

“…Here, it can be seen that the optimizer has designed shockfree supercritical cambered airfoils, while introducing wash out, namely, a gradual decrease in incidence angle from the root to the tip. The pressure coefficient distributions exhibit smooth pressure recoveries, which are favorable for maintaining attached boundary layers in viscous flow, in agreement with the findings of Osusky et al [47]. Note that the depicted airfoils have been rotated by the angle of attack so that the direction of streamwise flow is aligned with the xaxis.…”

“…As demonstrated by Osusky et al [47], the Euler equations tend to lead to the design of highly aft-loaded section shapes that are not of practical interest, given their susceptibility to boundary-layer separation. Although such a phenomenon does not have a large impact on the relative performance of the box wing, the omission of flow separation effects can be taken advantage of by the optimizer.…”

“…Following this work, Osusky et al [47] performed RANS-based aerodynamic shape optimization on a variety of planar wings, including that of the Common Research Model (CRM), a wing-body-tail configuration with a T-tail, and a blended wing-body configuration. Koo and Zingg [48] applied the algorithm to the CRM wing-body-tail configuration, in addition to several wingletted wings sized for the Boeing 737-900; these included a winglet up configuration, a wingtip fence configuration, and a split-tip configuration.…”

“…However, aerodynamic shape optimization at least based on the RANS equations will be necessary for capturing the intricacies of flow separation, a powerful and real phenomenon that can dictate the performance of an aircraft design [44,47]. The simulation of viscous effects will also allow the optimizer to account for the shorter chord lengths of the box-wing configuration, which may cause it to experience greater viscous drag compared to the cantilever wing.…”

“…The control points are then frozen while the parameterization is redefined by the grid node distribution of a grid suitable for computations of turbulent flows. The result is an algebraic approximation of the grid for turbulent flow that is not susceptible to control point cross-over [47].…”