Despite considerable research on aerodynamic shape optimization, there is no standard benchmark problem allowing researchers to compare results. This work addresses this issue by solving a series of aerodynamic shape optimization problems based on the Common Research Model wing benchmark case defined by the Aerodynamic Design Optimization Discussion Group. The aerodynamic model solves the Reynolds-averaged Navier-Stokes equations with a Spalart-Allmaras turbulence model. A gradient-based optimization algorithm is used in conjunction with an adjoint method that computes the required derivatives. The drag coefficient is minimized subject to lift, pitching moment, and geometric constraints. A multilevel technique is used to reduce the computational cost of the optimization. A single-point optimization is solved with 720 shape variables using a 28.8-million-cell mesh, reducing the drag by 8.5%. A more realistic design is achieved through a multipoint optimization. Multiple local minima are found when starting from multiple randomly generated geometries, but the minimum drag values are within 0.1 drag counts of each other, and the geometries differ by only 0.4% of the mean aerodynamic chord. The effect of varying the number of shape design variables is examined. The Common Research Model wing benchmark problem proved to be useful for evaluating our design optimization framework, and the geometries and meshes for both the baseline and optimized wings are available as supplemental materials in this paper.

The blended-wing body is an aircraft configuration that has the potential to be more efficient than conventional large transport aircraft configurations with the same capability. However, the design of the blended-wing is challenging due to the tight coupling between aerodynamic performance, trim, and stability. Other design challenges include the nature and number of the design variables involved, and the transonic flow conditions. To address these issues, we perform a series of aerodynamic shape optimization studies using Reynolds-averaged Navier-Stokes computational fluid dynamics with a Spalart-Allmaras turbulence model. A gradient-based optimization algorithm is used in conjunction with a discrete adjoint method that computes the derivatives of the aerodynamic forces. A total of 273 design variables-twist, airfoil shape, sweep, chord, and span-are considered. The drag coefficient at the cruise condition is minimized subject to lift, trim, static margin, and center plane bending moment constraints. The studies investigate the impact of the various constraints and design variables on optimized blended-wing-body configurations. The lowest drag among the trimmed and stable configurations is obtained by enforcing a 1% static margin constraint, resulting in a nearly elliptical spanwise lift distribution. Trim and static stability are investigated at both on-and off-design flight conditions. The single-point designs are relatively robust to the flight conditions, but further robustness is achieved through a multi-point optimization.

This paper presents an approach for the rapid implementation of an adjoint solver for the ReynoldsAveraged Navier-Stokes equations with a Spalart-Allmaras turbulence model. Automatic differentiation is used to construct the partial derivatives required in the adjoint formulation. The resulting adjoint implementation is computationally efficient and highly accurate. The assembly of each partial derivative in the adjoint formulation is discussed. In addition, a coloring acceleration technique is presented to improve the adjoint efficiency. The RANS adjoint is verified with complex-step method using a flow over a bump case. The RANS-based aerodynamic shape optimization of an ONERA M6 wing is also presented to demonstrate the aerodynamic shape optimization capability. The drag coefficient is reduced by 19% when subject to a lift coefficient constraint. The results are compared with Euler-based aerodynamic shape optimization and previous work. Finally, the effects of the frozenturbulence assumption on the accuracy and computational cost are assessed.

Adaptive morphing trailing edge wings have the potential to reduce the fuel burn of transport aircraft. In this paper, we quantify the aerodynamic performance benefits of a morphing trailing using aerodynamic design optimization. The aerodynamic model solves the Reynolds-averaged Navier-Stokes equations with a Spalart-Allmaras turbulence model. A gradient-based optimization algorithm is used in conjunction with an adjoint method that computes the required derivatives. The baseline geometry is optimized using a multipoint formulation with 192 shape design variables. The drag coefficient is minimized subject to lift, pitching moment, geometric constraints, and a 2.5 g maneuver bending moment constraint. The trailing edge of the wing is optimized based on the multipoint optimized wing. The trailing edge morphing is parameterized using 90 design variables that are optimized independently for each flight condition. A total of 407 trailing edge optimizations are performed with different flight conditions to span the entire flight envelope. We observed 1% drag reduction at on-design conditions, and 5% drag reduction near off-design conditions. The effectiveness of the trailing edge morphing is demonstrated by comparing with the optimized results of a hypothetical fully morphing wing. In addition, we compute the fuel burn reductions for a number of flights using the optimization results. A 1% cruise fuel burn reduction is achieved using adaptive morphing trailing edge for a typical long-haul twin-aisle mission.

Wing shape is one of the main drivers of aircraft aerodynamic performance, so most aerodynamic shape optimization efforts have been focused solely on the wing. However, the performance of the full aircraft configuration must account for the fact that the aircraft needs to be trimmed. Thus, to realize the full benefit of aerodynamic shape optimization, one should optimize the wing shape while including the full configuration and a trim constraint. To evaluate the benefit of this approach, we perform the aerodynamic shape optimization of the Common Research Model wing-body-tail configuration using gradient-based optimization with a Reynolds-averaged Navier-Stokes (RANS) model that includes a discrete adjoint implementation. We investigate the aerodynamic shape optimization of the wing with a trim constraint that is satisfied by rotating the horizontal tail. We optimize the same wing-body configuration without the tail, but with an added trim drag penalty based on a surrogate model we created. We also conduct the simultaneous aerodynamic shape optimization of both the wing and the horizontal-tail to investigate the benefit of optimizing the tail shape. The design variables consist of 816 wing shape variables and 144 horizontal tail shape variables, as well as the tail rotation angle and the aircraft angle of attack. The drag coefficient is minimized subject to lift and trim constraints. In addition, 1000 geometric thickness constraints and a wing volume constraint are enforced to guarantee that the wing thickness and volume values are no lower than those of the baseline geometry. We found that considering the trim during optimization is a better approach than using a fixed wing moment constraint. We also showed that the trim drag surrogate model we created can be used to yield a design whose drag coefficient is within 1.2 counts of that of an optimization where trim is satisfied with a rotating tail. However, we recommend the simultaneous optimization of wing and tail rotation to obtain the best possible performance.