Gradient-based Aerodynamic Shape Optimization Research Articles

Gradient-based aerodynamic shape optimization using a discrete adjoint approach on a graphics processing unit

Gradient-based aerodynamic shape optimization using a discrete adjoint approach on a graphics processing unit

Aerodynamic optimization with large shape and topology changes using a differentiable embedded boundary method

Embedded (or immersed) boundary methods (EBMs) for CFD and fluid-structure interaction (FSI) are attractive for aerodynamic optimization problems characterized by large shape deformations and surface topology changes. At each iteration, they eliminate the need for explicitly remeshing a computational fluid domain and avoid the pitfalls of transferring information from one CFD mesh to another. However, they are vulnerable to discrete events that compromise the smoothness of the aerodynamic objective and/or constraint functions they may compute. For this reason, the realization of EBMs for gradient-based aerodynamic shape optimization requires first their endowment with sufficient smoothness guarantees. Drawing on a recently developed EBM for the solution of compressible viscous fluid and FSI problems with such guarantees, this paper demonstrates the potential of shape-differentiable EBMs for discovering optimal aerodynamic designs featuring significant shape deformations and surface topology changes. Specifically, it highlights their advantages in terms of reliability with respect to large shape adjustments and surface topology changes, efficiency, simplicity, and reduced need for user intervention. To this end, the paper showcases the application of an advanced EBM with smoothness guarantees to wing shape, wing section, and nacelle-pylon placement optimization problems formulated for a NASA Common Research Model (CRM).

Aerodynamic Design Optimization of a Transonic Strut-Braced-Wing Regional Aircraft

The aerodynamic design and fuel burn performance of a Mach-0.78 strut-braced-wing regional jet is investigated through aerodynamic shape optimization based on the Reynolds-averaged Navier–Stokes equations. Conceptual-level multidisciplinary design optimization is first performed to size the strut-braced-wing aircraft for a design mission similar to the Embraer E190-E2, with a design range of 3100 nmi at a maximum capacity of 104 passengers, and a maximum payload of 30,200 lb. For direct performance comparisons, a conventional tube-and-wing regional jet is also sized and optimized based on the same reference aircraft. Gradient-based aerodynamic shape optimization is then performed on wing–body–tail models of each aircraft, with the objective of drag minimization at cruise over a 500 nmi nominal mission. Design variables include twist and section shape degrees of freedom, which are realized through a free-form and axial deformation geometry control system, whereas nonlinear constraints include constant lift, zero pitching moment, minimum wing volume, and minimum maximum thickness-to-chord ratios. Results indicate that the optimizer is capable of mitigating shock formation, boundary-layer separation, and other flow interference effects from each wing design, including those within the wing–strut junction of the strut-braced wing. With year 2020 technology levels, the strut-braced-wing regional jet offers a 12.9% improvement in cruise lift-to-drag ratio over an Embraer E190-E2-like conventional tube-and-wing aircraft, which translates to a 7.6% reduction in block fuel for the nominal mission.

On an Exact Step Length in Gradient-Based Aerodynamic Shape Optimization—Part II: Viscous Flows

This study presents an extension of a previous study (On an Exact Step Length in Gradient-Based Aerodynamic Shape Optimization) to viscous transonic flows. In this work, we showed that the same procedure to derive an explicit expression for an exact step length βexact in a gradient-based optimization method for inviscid transonic flows can be employed for viscous transonic flows. The extended numerical method was evaluated for the viscous flows over the transonic RAE 2822 airfoil at two common flow conditions in the transonic regime. To do so, the RAE 2822 airfoil was reconstructed by a Bezier curve of degree 16. The numerical solution of the transonic turbulent flow over the airfoil was performed using the solver ANSYS Fluent (using the Spalart–Allmaras turbulence model). Using the proposed step length, a gradient-based optimization method was employed to minimize the drag-to-lift ratio of the airfoil. The gradient of the objective function with respect to design variables was calculated by the finite-difference method. Efficiency and accuracy of the proposed method were investigated through two test cases.

Efficient Mesh Generation and Deformation for Aerodynamic Shape Optimization

Mesh generation and deformation are critical elements in gradient-based aerodynamic shape optimization (ASO). Improperly generated or deformed meshes may contain bad-quality cells that degrade the accuracy of computational fluid dynamics (CFD) solvers. Moreover, an inefficient mesh deformation method can become the bottleneck for the entire ASO process. To perform practical ASO, mesh generation and deformation methods need to be automated, scalable, robust, and computationally efficient. This paper tackles these challenges by developing an efficient approach for generating high-quality structured meshes in a semi-automatic manner. An automatic mesh generation approach is also proposed to handle intersections of multiple structured meshes with the overset mesh approach. In addition to mesh generation, a flexible mesh deformation method is developed, along with an efficient approach for computing mesh deformation derivatives using automatic differentiation. Finally, the performance of the proposed approaches is evaluated in terms of speed, scalability, and robustness. The mesh generation approach scales up to 100 million cells and 256 CPU cores. In addition, the robust mesh deformation approach enables a large range of valid mesh deformations, which gives more freedom to explore the design space in ASO. Moreover, the mesh deformation and the computation of its derivatives require only 0.1% of the CFD runtime. The mesh generation and deformation approaches have been implemented in the pyHyp and IDWarp software packages, which are publicly available under open-source licenses. The proposed approaches are useful tools to handle general ASO problems for aircraft, turbomachinery, and ground vehicles.

Adjoint-based aerodynamic shape optimization including transition to turbulence effects

The inclusion of transition to turbulence effects in aerodynamic shape optimization makes it possible to use it as a tool for the design of airframes with laminar flow. Modified Reynolds-Averaged Navier–Stokes (RANS) models that consider transition to turbulence have gained traction in the computational fluid dynamics (CFD) community. These models enable the computation of transitional flows without the need for external modules. In this work, we use a smooth version of the amplification factor transport (AFT) model, called AFT-S, to perform gradient-based aerodynamic shape optimization (ASO) of airfoils in subsonic and transonic flow conditions. We investigate the benefits of including transition effects into the optimization process and assess the impact of losing laminar flow when early transition to turbulence occurs due to surface contamination. Our results indicate that our design optimization approach yields lower drag airfoils when transition effects are considered. For the transonic case, the optimizer trades between shock wave strength and laminar flow extension to minimize drag.

A reduced-order model for gradient-based aerodynamic shape optimisation

This work presents a reduced order model for gradient based aerodynamic shape optimization. The solution of the fluid Euler equations is converted to reduced Newton iterations by using the Least Squares Petrov-Galerkin projection. The reduced order basis is extracted by Proper Orthogonal Decomposition from snapshots based on the fluid state. The formulation distinguishes itself by obtaining the snapshots for all design parameters by solving a linear system of equations. Similarly, the reduced gradient formulation is derived by projecting the full-order model state onto the subspace spanned by the reduced basis. Auto-differentiation is used to evaluate the reduced Jacobian without forming the full fluid Jacobian explicitly during the reduced Newton iterations. Throughout the optimisation trajectory, the residual of the reduced Newton iterations is used as an indicator to update the snapshots and enrich the reduced order basis. The resulting multi-fidelity optimisation problem is managed by a trust-region algorithm. The ROM is demonstrated for a subsonic inverse design problem and for an aerofoil drag minimization problem in the transonic regime. The results suggest that the proposed algorithm is capable of aerodynamic shape optimization while reducing the number of full-order model queries and time to solution with respect to an adjoint gradient based optimisation framework.

Aerodynamic Design and Shape Optimization with the Far-Field Drag Decomposition Approach

In the aerodynamic shape design, the drag prediction has always been an extremely challenging mission for the exploration of a configuration. As for the more complex configurations, it is especially desired to the availability of a highly accurate and reliable aerodynamic numerical solution. For improving the drag prediction accuracy and promoting the aerodynamic shape designs, firstly, the characteristics of drag prediction based on far-field drag method and near-field drag method is analyzed and compared. Also, the merits and demerits of defining axial velocity defect with the current main far-field drag prediction approaches is summarized, which promotes the building of the improved method of axial velocity defect and the improved far-field drag prediction and decomposition approach. Moreover, during the establishment of the drag decomposition method, it is necessary to judge and decide on the selection of the drag region. Therefore, the discussions on the sensitivity of the relevant parameters are fulfilled. Furthermore, based on the far-field drag prediction and decomposition method constructed, the aerodynamic performance research of Common Research Model wing-body configuration is launched. The results show that it can effectively observe and analyze the changes in drag components, their impact on the total drag and the contribution percentage. Finally, combining the far-field drag prediction and decomposition method proposed in this paper with a gradient-based aerodynamic shape optimization design system, the aerodynamic shape optimization designs are studied with CRM wing-body configuration. The results can not only directly analyze the detailed change of the visualized drag region, but also can obtain the more accurate total drag and lift-to-drag ratio of the optimized configuration by removing the spurious drag.

On an Exact Step Length in Gradient-Based Aerodynamic Shape Optimization

This study proposeda novel exact expression for step length (size) in gradient-based aerodynamic shape optimization for an airfoil in steady inviscid transonic flows. The airfoil surfaces were parameterized using Bezier curves. The Bezier curve control points were considered as design variables and the finite-difference method was used to compute the gradient of the objective function (drag-to-lift ratio) with respect to the design variables. An exact explicit expression was derived for the step length in gradient-based shape optimization problems. It was shown that the derived step length was independent of the method used for calculating the gradient (adjoint method, finite-difference method, etc.). The obtained results reveal the accuracy of the derived step length.

Optimal Aerodynamic Shape Optimization of a Paraglider Airfoil Based on the Sharknose Concept

The effects of classical air inlet configurations on the aerodynamic performance of a paraglider airfoil are firstly presented. Followed by conducting gradient-based aerodynamic shape optimization of the baseline airfoil used in the investigation of the classical air inlets. Different air inlet configurations are introduced to the optimized profile, and there effects on the aerodynamic performance are then compared to the initial and optimized airfoils. The Reynolds averaged Navier-Stokes equations (RANS) are solved for the flow field around the closed and open airfoils. The canopy is assumed to be smooth, rigid and impermeable. Results are focused on both of lift and drag coefficients for performance analysis and on the internal pressure coefficient which can be critical for a real flexible wing regarding the risk of collapse.

Unsteady Continuous Adjoint Approach for Aerodynamic Design on Dynamic Meshes

This paper presents the development and application of a new unsteady continuous adjoint formulation for optimal shape design of aerodynamic surfaces in motion, such as rotating or pitching applications. The arbitrary Lagrangian–Eulerian form of the unsteady, compressible Reynolds-averaged Navier–Stokes equations with a generic source term is considered, and from these governing flow equations, an adjoint formulation centered around finding surface sensitivities using shape calculus is derived. This surface formulation provides the gradient information necessary for performing gradient-based aerodynamic shape optimization at a computational cost equivalent to solving the flow equations and with minimal memory overhead. To verify the methodology, gradients provided by the continuous adjoint and finite-differencing approaches are compared. Optimal shape design is demonstrated in both two and three dimensions for pitching airfoil and wing test cases.

Mesh deformation using radial basis functions for gradient-based aerodynamic shape optimization

Gradient-based aerodynamic shape optimization using computational fluid dynamics (CFD), and time dependent problems in aeroelasticity, that is, coupled calculations between computational structural mechanics (CSM) and CFD, require repeated deformations of the CFD mesh. An interpolation scheme, based on radial basis functions (RBF), is devised in order to propagate the deformations from the boundaries to the interior of the CFD mesh. This method can lower the computational costs due to the deformation of the mesh, in comparison with the usual Laplace smoothing. Moreover, the algorithm is independent of the mesh connectivities. Therefore, structured and unstructured meshes are equally treated as well as hybrid meshes. The application of this interpolation scheme in problems of aerodynamic shape optimization is also carefully investigated. When the optimization is executed by a gradient-based algorithm the cost function is differentiated with respect to the design parameters in order to obtain the gradient. The gradient is most efficiently and accurately calculated by solving a certain adjoint equation derived from the discretized flow equations. The calculation of the gradient, which is detailed in this presentation, involves the Jacobian matrix of the mesh deformation. Finally, we present the results of an optimization of the ONERA M6 wing at transonic speed using the interpolation algorithm. The results are used for comparison with another technique of mesh deformation. The quality of the mesh obtained by the new algorithm, and the interpolation error, are analyzed with respect to the parameters of the interpolation scheme: the type of RBF, the RBF’s shape parameter, and the sets of control points.